Arithmetic of Rikuna’s generic cyclic polynomial and generalization of Kummer theory

Abstract. In this paper we study the arithmetic of the Rikuna’s generic polynomial for the cyclic group of order n and obtain a generalized Kummer theory. It is useful under the condition that and ω∈k where ζ is a primitive n-th root of unity and ω=ζ+$ ζ^{−1} $. In particular, this result with ζ∈k i...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Komatsu, Toru [verfasserIn]

Format:	Artikel
Sprache:	Englisch

Erschienen:	2004

Schlagwörter:	Cyclic Group Generic Polynomial Kummer Theory Cyclic Polynomial

Systematik:	SA 6730 SA 6730

Anmerkung:	© Springer-Verlag Berlin Heidelberg 2004

Übergeordnetes Werk:	Enthalten in: Manuscripta mathematica - Springer-Verlag, 1969, 114(2004), 3 vom: 14. Juni, Seite 265-279
Übergeordnetes Werk:	volume:114 ; year:2004 ; number:3 ; day:14 ; month:06 ; pages:265-279

Links:	Volltext

DOI / URN:	10.1007/s00229-004-0460-2

Katalog-ID:	OLC2061285309

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allfields	10.1007/s00229-004-0460-2 doi (DE-627)OLC2061285309 (DE-He213)s00229-004-0460-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 6730 VZ rvk SA 6730 VZ rvk Komatsu, Toru verfasserin aut Arithmetic of Rikuna’s generic cyclic polynomial and generalization of Kummer theory 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. In this paper we study the arithmetic of the Rikuna’s generic polynomial for the cyclic group of order n and obtain a generalized Kummer theory. It is useful under the condition that and ω∈k where ζ is a primitive n-th root of unity and ω=ζ+$ ζ^{−1} $. In particular, this result with ζ∈k implies the classical Kummer theory. Cyclic Group Generic Polynomial Kummer Theory Cyclic Polynomial Enthalten in Manuscripta mathematica Springer-Verlag, 1969 114(2004), 3 vom: 14. Juni, Seite 265-279 (DE-627)129081388 (DE-600)3448-4 (DE-576)014414244 0025-2611 nnns volume:114 year:2004 number:3 day:14 month:06 pages:265-279 https://doi.org/10.1007/s00229-004-0460-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_100 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4029 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 SA 6730 SA 6730 AR 114 2004 3 14 06 265-279
spelling	10.1007/s00229-004-0460-2 doi (DE-627)OLC2061285309 (DE-He213)s00229-004-0460-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 6730 VZ rvk SA 6730 VZ rvk Komatsu, Toru verfasserin aut Arithmetic of Rikuna’s generic cyclic polynomial and generalization of Kummer theory 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. In this paper we study the arithmetic of the Rikuna’s generic polynomial for the cyclic group of order n and obtain a generalized Kummer theory. It is useful under the condition that and ω∈k where ζ is a primitive n-th root of unity and ω=ζ+$ ζ^{−1} $. In particular, this result with ζ∈k implies the classical Kummer theory. Cyclic Group Generic Polynomial Kummer Theory Cyclic Polynomial Enthalten in Manuscripta mathematica Springer-Verlag, 1969 114(2004), 3 vom: 14. Juni, Seite 265-279 (DE-627)129081388 (DE-600)3448-4 (DE-576)014414244 0025-2611 nnns volume:114 year:2004 number:3 day:14 month:06 pages:265-279 https://doi.org/10.1007/s00229-004-0460-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_100 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4029 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 SA 6730 SA 6730 AR 114 2004 3 14 06 265-279
allfields_unstemmed	10.1007/s00229-004-0460-2 doi (DE-627)OLC2061285309 (DE-He213)s00229-004-0460-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 6730 VZ rvk SA 6730 VZ rvk Komatsu, Toru verfasserin aut Arithmetic of Rikuna’s generic cyclic polynomial and generalization of Kummer theory 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. In this paper we study the arithmetic of the Rikuna’s generic polynomial for the cyclic group of order n and obtain a generalized Kummer theory. It is useful under the condition that and ω∈k where ζ is a primitive n-th root of unity and ω=ζ+$ ζ^{−1} $. In particular, this result with ζ∈k implies the classical Kummer theory. Cyclic Group Generic Polynomial Kummer Theory Cyclic Polynomial Enthalten in Manuscripta mathematica Springer-Verlag, 1969 114(2004), 3 vom: 14. Juni, Seite 265-279 (DE-627)129081388 (DE-600)3448-4 (DE-576)014414244 0025-2611 nnns volume:114 year:2004 number:3 day:14 month:06 pages:265-279 https://doi.org/10.1007/s00229-004-0460-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_100 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4029 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 SA 6730 SA 6730 AR 114 2004 3 14 06 265-279
allfieldsGer	10.1007/s00229-004-0460-2 doi (DE-627)OLC2061285309 (DE-He213)s00229-004-0460-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 6730 VZ rvk SA 6730 VZ rvk Komatsu, Toru verfasserin aut Arithmetic of Rikuna’s generic cyclic polynomial and generalization of Kummer theory 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. In this paper we study the arithmetic of the Rikuna’s generic polynomial for the cyclic group of order n and obtain a generalized Kummer theory. It is useful under the condition that and ω∈k where ζ is a primitive n-th root of unity and ω=ζ+$ ζ^{−1} $. In particular, this result with ζ∈k implies the classical Kummer theory. Cyclic Group Generic Polynomial Kummer Theory Cyclic Polynomial Enthalten in Manuscripta mathematica Springer-Verlag, 1969 114(2004), 3 vom: 14. Juni, Seite 265-279 (DE-627)129081388 (DE-600)3448-4 (DE-576)014414244 0025-2611 nnns volume:114 year:2004 number:3 day:14 month:06 pages:265-279 https://doi.org/10.1007/s00229-004-0460-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_100 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4029 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 SA 6730 SA 6730 AR 114 2004 3 14 06 265-279
allfieldsSound	10.1007/s00229-004-0460-2 doi (DE-627)OLC2061285309 (DE-He213)s00229-004-0460-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 6730 VZ rvk SA 6730 VZ rvk Komatsu, Toru verfasserin aut Arithmetic of Rikuna’s generic cyclic polynomial and generalization of Kummer theory 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. In this paper we study the arithmetic of the Rikuna’s generic polynomial for the cyclic group of order n and obtain a generalized Kummer theory. It is useful under the condition that and ω∈k where ζ is a primitive n-th root of unity and ω=ζ+$ ζ^{−1} $. In particular, this result with ζ∈k implies the classical Kummer theory. Cyclic Group Generic Polynomial Kummer Theory Cyclic Polynomial Enthalten in Manuscripta mathematica Springer-Verlag, 1969 114(2004), 3 vom: 14. Juni, Seite 265-279 (DE-627)129081388 (DE-600)3448-4 (DE-576)014414244 0025-2611 nnns volume:114 year:2004 number:3 day:14 month:06 pages:265-279 https://doi.org/10.1007/s00229-004-0460-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_100 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4029 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 SA 6730 SA 6730 AR 114 2004 3 14 06 265-279
language	English
source	Enthalten in Manuscripta mathematica 114(2004), 3 vom: 14. Juni, Seite 265-279 volume:114 year:2004 number:3 day:14 month:06 pages:265-279
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topic_facet	Cyclic Group Generic Polynomial Kummer Theory Cyclic Polynomial
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author	Komatsu, Toru
spellingShingle	Komatsu, Toru ddc 510 ssgn 17,1 rvk SA 6730 misc Cyclic Group misc Generic Polynomial misc Kummer Theory misc Cyclic Polynomial Arithmetic of Rikuna’s generic cyclic polynomial and generalization of Kummer theory
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title	Arithmetic of Rikuna’s generic cyclic polynomial and generalization of Kummer theory
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title_full	Arithmetic of Rikuna’s generic cyclic polynomial and generalization of Kummer theory
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title_sort	arithmetic of rikuna’s generic cyclic polynomial and generalization of kummer theory
title_auth	Arithmetic of Rikuna’s generic cyclic polynomial and generalization of Kummer theory
abstract	Abstract. In this paper we study the arithmetic of the Rikuna’s generic polynomial for the cyclic group of order n and obtain a generalized Kummer theory. It is useful under the condition that and ω∈k where ζ is a primitive n-th root of unity and ω=ζ+$ ζ^{−1} $. In particular, this result with ζ∈k implies the classical Kummer theory. © Springer-Verlag Berlin Heidelberg 2004
abstractGer	Abstract. In this paper we study the arithmetic of the Rikuna’s generic polynomial for the cyclic group of order n and obtain a generalized Kummer theory. It is useful under the condition that and ω∈k where ζ is a primitive n-th root of unity and ω=ζ+$ ζ^{−1} $. In particular, this result with ζ∈k implies the classical Kummer theory. © Springer-Verlag Berlin Heidelberg 2004
abstract_unstemmed	Abstract. In this paper we study the arithmetic of the Rikuna’s generic polynomial for the cyclic group of order n and obtain a generalized Kummer theory. It is useful under the condition that and ω∈k where ζ is a primitive n-th root of unity and ω=ζ+$ ζ^{−1} $. In particular, this result with ζ∈k implies the classical Kummer theory. © Springer-Verlag Berlin Heidelberg 2004
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title_short	Arithmetic of Rikuna’s generic cyclic polynomial and generalization of Kummer theory
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