Rational formulas for traces in zero-dimensional algebras

Abstract We present a rational expression for the trace of the multiplication map $ Times_{r} $ : A → A in a finite-dimensional algebra %${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}%$ in terms of the generalized Chow form of %${\mathcal{I}}%$ . Here, %${\mathcal{I} \subset \mathbb {K}[x_1,\ldot...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	D’Andrea, Carlos [verfasserIn] Jeronimo, Gabriela

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2008

Schlagwörter:	Complete Intersection Characteristic Zero Trace Formula Irreducible Polynomial Zero Divisor

Anmerkung:	© Springer-Verlag 2008

Übergeordnetes Werk:	Enthalten in: Applicable algebra in engineering, communication and computing - Berlin : Springer, 1990, 19(2008), 6 vom: 26. Nov.
Übergeordnetes Werk:	volume:19 ; year:2008 ; number:6 ; day:26 ; month:11

Links:	Volltext

DOI / URN:	10.1007/s00200-008-0085-x

Katalog-ID:	SPR001756494

Internformat


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520			\|a Abstract We present a rational expression for the trace of the multiplication map $ Times_{r} $ : A → A in a finite-dimensional algebra %${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}%$ in terms of the generalized Chow form of %${\mathcal{I}}%$ . Here, %${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}%$ is a zero-dimensional ideal, %${\mathbb {K}}%$ is a field of characteristic zero, and r(x1,..., xn) a rational function whose denominator is not a zero divisor in A. If %${\mathcal {I}}%$ is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants.
650		4	\|a Complete Intersection \|7 (dpeaa)DE-He213
650		4	\|a Characteristic Zero \|7 (dpeaa)DE-He213
650		4	\|a Trace Formula \|7 (dpeaa)DE-He213
650		4	\|a Irreducible Polynomial \|7 (dpeaa)DE-He213
650		4	\|a Zero Divisor \|7 (dpeaa)DE-He213
700	1		\|a Jeronimo, Gabriela \|4 aut
773	0	8	\|i Enthalten in \|t Applicable algebra in engineering, communication and computing \|d Berlin : Springer, 1990 \|g 19(2008), 6 vom: 26. Nov. \|w (DE-627)253389909 \|w (DE-600)1458434-7 \|x 1432-0622 \|7 nnns
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912			\|a GBV_USEFLAG_A
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912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_101
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_267
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4277
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
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Indexfelder

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matchkey_str	article:14320622:2008----::ainlomlsotaeizrdmn
hierarchy_sort_str	2008
publishDate	2008
allfields	10.1007/s00200-008-0085-x doi (DE-627)SPR001756494 (SPR)s00200-008-0085-x-e DE-627 ger DE-627 rakwb eng D’Andrea, Carlos verfasserin aut Rational formulas for traces in zero-dimensional algebras 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract We present a rational expression for the trace of the multiplication map $ Times_{r} $ : A → A in a finite-dimensional algebra %${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}%$ in terms of the generalized Chow form of %${\mathcal{I}}%$ . Here, %${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}%$ is a zero-dimensional ideal, %${\mathbb {K}}%$ is a field of characteristic zero, and r(x1,..., xn) a rational function whose denominator is not a zero divisor in A. If %${\mathcal {I}}%$ is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants. Complete Intersection (dpeaa)DE-He213 Characteristic Zero (dpeaa)DE-He213 Trace Formula (dpeaa)DE-He213 Irreducible Polynomial (dpeaa)DE-He213 Zero Divisor (dpeaa)DE-He213 Jeronimo, Gabriela aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 19(2008), 6 vom: 26. Nov. (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:19 year:2008 number:6 day:26 month:11 https://dx.doi.org/10.1007/s00200-008-0085-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 19 2008 6 26 11
spelling	10.1007/s00200-008-0085-x doi (DE-627)SPR001756494 (SPR)s00200-008-0085-x-e DE-627 ger DE-627 rakwb eng D’Andrea, Carlos verfasserin aut Rational formulas for traces in zero-dimensional algebras 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract We present a rational expression for the trace of the multiplication map $ Times_{r} $ : A → A in a finite-dimensional algebra %${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}%$ in terms of the generalized Chow form of %${\mathcal{I}}%$ . Here, %${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}%$ is a zero-dimensional ideal, %${\mathbb {K}}%$ is a field of characteristic zero, and r(x1,..., xn) a rational function whose denominator is not a zero divisor in A. If %${\mathcal {I}}%$ is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants. Complete Intersection (dpeaa)DE-He213 Characteristic Zero (dpeaa)DE-He213 Trace Formula (dpeaa)DE-He213 Irreducible Polynomial (dpeaa)DE-He213 Zero Divisor (dpeaa)DE-He213 Jeronimo, Gabriela aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 19(2008), 6 vom: 26. Nov. (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:19 year:2008 number:6 day:26 month:11 https://dx.doi.org/10.1007/s00200-008-0085-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 19 2008 6 26 11
allfields_unstemmed	10.1007/s00200-008-0085-x doi (DE-627)SPR001756494 (SPR)s00200-008-0085-x-e DE-627 ger DE-627 rakwb eng D’Andrea, Carlos verfasserin aut Rational formulas for traces in zero-dimensional algebras 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract We present a rational expression for the trace of the multiplication map $ Times_{r} $ : A → A in a finite-dimensional algebra %${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}%$ in terms of the generalized Chow form of %${\mathcal{I}}%$ . Here, %${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}%$ is a zero-dimensional ideal, %${\mathbb {K}}%$ is a field of characteristic zero, and r(x1,..., xn) a rational function whose denominator is not a zero divisor in A. If %${\mathcal {I}}%$ is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants. Complete Intersection (dpeaa)DE-He213 Characteristic Zero (dpeaa)DE-He213 Trace Formula (dpeaa)DE-He213 Irreducible Polynomial (dpeaa)DE-He213 Zero Divisor (dpeaa)DE-He213 Jeronimo, Gabriela aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 19(2008), 6 vom: 26. Nov. (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:19 year:2008 number:6 day:26 month:11 https://dx.doi.org/10.1007/s00200-008-0085-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 19 2008 6 26 11
allfieldsGer	10.1007/s00200-008-0085-x doi (DE-627)SPR001756494 (SPR)s00200-008-0085-x-e DE-627 ger DE-627 rakwb eng D’Andrea, Carlos verfasserin aut Rational formulas for traces in zero-dimensional algebras 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract We present a rational expression for the trace of the multiplication map $ Times_{r} $ : A → A in a finite-dimensional algebra %${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}%$ in terms of the generalized Chow form of %${\mathcal{I}}%$ . Here, %${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}%$ is a zero-dimensional ideal, %${\mathbb {K}}%$ is a field of characteristic zero, and r(x1,..., xn) a rational function whose denominator is not a zero divisor in A. If %${\mathcal {I}}%$ is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants. Complete Intersection (dpeaa)DE-He213 Characteristic Zero (dpeaa)DE-He213 Trace Formula (dpeaa)DE-He213 Irreducible Polynomial (dpeaa)DE-He213 Zero Divisor (dpeaa)DE-He213 Jeronimo, Gabriela aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 19(2008), 6 vom: 26. Nov. (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:19 year:2008 number:6 day:26 month:11 https://dx.doi.org/10.1007/s00200-008-0085-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 19 2008 6 26 11
allfieldsSound	10.1007/s00200-008-0085-x doi (DE-627)SPR001756494 (SPR)s00200-008-0085-x-e DE-627 ger DE-627 rakwb eng D’Andrea, Carlos verfasserin aut Rational formulas for traces in zero-dimensional algebras 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2008 Abstract We present a rational expression for the trace of the multiplication map $ Times_{r} $ : A → A in a finite-dimensional algebra %${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}%$ in terms of the generalized Chow form of %${\mathcal{I}}%$ . Here, %${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}%$ is a zero-dimensional ideal, %${\mathbb {K}}%$ is a field of characteristic zero, and r(x1,..., xn) a rational function whose denominator is not a zero divisor in A. If %${\mathcal {I}}%$ is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants. Complete Intersection (dpeaa)DE-He213 Characteristic Zero (dpeaa)DE-He213 Trace Formula (dpeaa)DE-He213 Irreducible Polynomial (dpeaa)DE-He213 Zero Divisor (dpeaa)DE-He213 Jeronimo, Gabriela aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 19(2008), 6 vom: 26. Nov. (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:19 year:2008 number:6 day:26 month:11 https://dx.doi.org/10.1007/s00200-008-0085-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 19 2008 6 26 11
language	English
source	Enthalten in Applicable algebra in engineering, communication and computing 19(2008), 6 vom: 26. Nov. volume:19 year:2008 number:6 day:26 month:11
sourceStr	Enthalten in Applicable algebra in engineering, communication and computing 19(2008), 6 vom: 26. Nov. volume:19 year:2008 number:6 day:26 month:11
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Complete Intersection Characteristic Zero Trace Formula Irreducible Polynomial Zero Divisor
isfreeaccess_bool	false
container_title	Applicable algebra in engineering, communication and computing
authorswithroles_txt_mv	D’Andrea, Carlos @@aut@@ Jeronimo, Gabriela @@aut@@
publishDateDaySort_date	2008-11-26T00:00:00Z
hierarchy_top_id	253389909
id	SPR001756494
language_de	englisch
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author	D’Andrea, Carlos
spellingShingle	D’Andrea, Carlos misc Complete Intersection misc Characteristic Zero misc Trace Formula misc Irreducible Polynomial misc Zero Divisor Rational formulas for traces in zero-dimensional algebras
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topic_title	Rational formulas for traces in zero-dimensional algebras Complete Intersection (dpeaa)DE-He213 Characteristic Zero (dpeaa)DE-He213 Trace Formula (dpeaa)DE-He213 Irreducible Polynomial (dpeaa)DE-He213 Zero Divisor (dpeaa)DE-He213
topic	misc Complete Intersection misc Characteristic Zero misc Trace Formula misc Irreducible Polynomial misc Zero Divisor
topic_unstemmed	misc Complete Intersection misc Characteristic Zero misc Trace Formula misc Irreducible Polynomial misc Zero Divisor
topic_browse	misc Complete Intersection misc Characteristic Zero misc Trace Formula misc Irreducible Polynomial misc Zero Divisor
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title	Rational formulas for traces in zero-dimensional algebras
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title_full	Rational formulas for traces in zero-dimensional algebras
author_sort	D’Andrea, Carlos
journal	Applicable algebra in engineering, communication and computing
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author_browse	D’Andrea, Carlos Jeronimo, Gabriela
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author-letter	D’Andrea, Carlos
doi_str_mv	10.1007/s00200-008-0085-x
title_sort	rational formulas for traces in zero-dimensional algebras
title_auth	Rational formulas for traces in zero-dimensional algebras
abstract	Abstract We present a rational expression for the trace of the multiplication map $ Times_{r} $ : A → A in a finite-dimensional algebra %${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}%$ in terms of the generalized Chow form of %${\mathcal{I}}%$ . Here, %${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}%$ is a zero-dimensional ideal, %${\mathbb {K}}%$ is a field of characteristic zero, and r(x1,..., xn) a rational function whose denominator is not a zero divisor in A. If %${\mathcal {I}}%$ is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants. © Springer-Verlag 2008
abstractGer	Abstract We present a rational expression for the trace of the multiplication map $ Times_{r} $ : A → A in a finite-dimensional algebra %${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}%$ in terms of the generalized Chow form of %${\mathcal{I}}%$ . Here, %${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}%$ is a zero-dimensional ideal, %${\mathbb {K}}%$ is a field of characteristic zero, and r(x1,..., xn) a rational function whose denominator is not a zero divisor in A. If %${\mathcal {I}}%$ is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants. © Springer-Verlag 2008
abstract_unstemmed	Abstract We present a rational expression for the trace of the multiplication map $ Times_{r} $ : A → A in a finite-dimensional algebra %${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}%$ in terms of the generalized Chow form of %${\mathcal{I}}%$ . Here, %${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}%$ is a zero-dimensional ideal, %${\mathbb {K}}%$ is a field of characteristic zero, and r(x1,..., xn) a rational function whose denominator is not a zero divisor in A. If %${\mathcal {I}}%$ is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants. © Springer-Verlag 2008
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title_short	Rational formulas for traces in zero-dimensional algebras
url	https://dx.doi.org/10.1007/s00200-008-0085-x
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up_date	2024-07-04T00:15:59.227Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR001756494</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230327135204.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2008 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00200-008-0085-x</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR001756494</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00200-008-0085-x-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">D’Andrea, Carlos</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Rational formulas for traces in zero-dimensional algebras</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2008</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag 2008</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We present a rational expression for the trace of the multiplication map $ Times_{r} $ : A → A in a finite-dimensional algebra %${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}%$ in terms of the generalized Chow form of %${\mathcal{I}}%$ . Here, %${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}%$ is a zero-dimensional ideal, %${\mathbb {K}}%$ is a field of characteristic zero, and r(x1,..., xn) a rational function whose denominator is not a zero divisor in A. 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