Some properties of retract lattices of monounary algebras

Abstract Necessary and sufficient conditions for a connected monounary algebra (A, f), under which the lattice R∅(A, f) of all retracts of (A, f) (together with ∅) is algebraic, are proved. Simultaneously, all connected monounary algebras in which each retract is a union of completely join-irreducib...
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Autor*in:	Jakubíková-Studenovská, Danica [verfasserIn] Pócs, Jozef

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2012

Schlagwörter:	monounary algebra retract retract lattice

Anmerkung:	© © Versita Warsaw and Springer-Verlag Wien 2012

Übergeordnetes Werk:	Enthalten in: Mathematica Slovaca - Warsaw : Versita, 2007, 62(2012), 2 vom: 29. Feb., Seite 169-186
Übergeordnetes Werk:	volume:62 ; year:2012 ; number:2 ; day:29 ; month:02 ; pages:169-186

Links:	Volltext

DOI / URN:	10.2478/s12175-012-0002-4

Katalog-ID:	SPR02542744X

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allfields	10.2478/s12175-012-0002-4 doi (DE-627)SPR02542744X (SPR)s12175-012-0002-4-e DE-627 ger DE-627 rakwb eng Jakubíková-Studenovská, Danica verfasserin aut Some properties of retract lattices of monounary algebras 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © © Versita Warsaw and Springer-Verlag Wien 2012 Abstract Necessary and sufficient conditions for a connected monounary algebra (A, f), under which the lattice R∅(A, f) of all retracts of (A, f) (together with ∅) is algebraic, are proved. Simultaneously, all connected monounary algebras in which each retract is a union of completely join-irreducible elements of R∅(A, f) are characterized. Further, there are described all connected monounary algebras (A, f) such that the lattice R∅(A, f) is complemented. In this case R∅(A, f) forms a boolean lattice. monounary algebra (dpeaa)DE-He213 retract (dpeaa)DE-He213 retract lattice (dpeaa)DE-He213 Pócs, Jozef aut Enthalten in Mathematica Slovaca Warsaw : Versita, 2007 62(2012), 2 vom: 29. Feb., Seite 169-186 (DE-627)548127344 (DE-600)2393408-6 1337-2211 nnns volume:62 year:2012 number:2 day:29 month:02 pages:169-186 https://dx.doi.org/10.2478/s12175-012-0002-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 62 2012 2 29 02 169-186
spelling	10.2478/s12175-012-0002-4 doi (DE-627)SPR02542744X (SPR)s12175-012-0002-4-e DE-627 ger DE-627 rakwb eng Jakubíková-Studenovská, Danica verfasserin aut Some properties of retract lattices of monounary algebras 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © © Versita Warsaw and Springer-Verlag Wien 2012 Abstract Necessary and sufficient conditions for a connected monounary algebra (A, f), under which the lattice R∅(A, f) of all retracts of (A, f) (together with ∅) is algebraic, are proved. Simultaneously, all connected monounary algebras in which each retract is a union of completely join-irreducible elements of R∅(A, f) are characterized. Further, there are described all connected monounary algebras (A, f) such that the lattice R∅(A, f) is complemented. In this case R∅(A, f) forms a boolean lattice. monounary algebra (dpeaa)DE-He213 retract (dpeaa)DE-He213 retract lattice (dpeaa)DE-He213 Pócs, Jozef aut Enthalten in Mathematica Slovaca Warsaw : Versita, 2007 62(2012), 2 vom: 29. Feb., Seite 169-186 (DE-627)548127344 (DE-600)2393408-6 1337-2211 nnns volume:62 year:2012 number:2 day:29 month:02 pages:169-186 https://dx.doi.org/10.2478/s12175-012-0002-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 62 2012 2 29 02 169-186
allfields_unstemmed	10.2478/s12175-012-0002-4 doi (DE-627)SPR02542744X (SPR)s12175-012-0002-4-e DE-627 ger DE-627 rakwb eng Jakubíková-Studenovská, Danica verfasserin aut Some properties of retract lattices of monounary algebras 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © © Versita Warsaw and Springer-Verlag Wien 2012 Abstract Necessary and sufficient conditions for a connected monounary algebra (A, f), under which the lattice R∅(A, f) of all retracts of (A, f) (together with ∅) is algebraic, are proved. Simultaneously, all connected monounary algebras in which each retract is a union of completely join-irreducible elements of R∅(A, f) are characterized. Further, there are described all connected monounary algebras (A, f) such that the lattice R∅(A, f) is complemented. In this case R∅(A, f) forms a boolean lattice. monounary algebra (dpeaa)DE-He213 retract (dpeaa)DE-He213 retract lattice (dpeaa)DE-He213 Pócs, Jozef aut Enthalten in Mathematica Slovaca Warsaw : Versita, 2007 62(2012), 2 vom: 29. Feb., Seite 169-186 (DE-627)548127344 (DE-600)2393408-6 1337-2211 nnns volume:62 year:2012 number:2 day:29 month:02 pages:169-186 https://dx.doi.org/10.2478/s12175-012-0002-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 62 2012 2 29 02 169-186
allfieldsGer	10.2478/s12175-012-0002-4 doi (DE-627)SPR02542744X (SPR)s12175-012-0002-4-e DE-627 ger DE-627 rakwb eng Jakubíková-Studenovská, Danica verfasserin aut Some properties of retract lattices of monounary algebras 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © © Versita Warsaw and Springer-Verlag Wien 2012 Abstract Necessary and sufficient conditions for a connected monounary algebra (A, f), under which the lattice R∅(A, f) of all retracts of (A, f) (together with ∅) is algebraic, are proved. Simultaneously, all connected monounary algebras in which each retract is a union of completely join-irreducible elements of R∅(A, f) are characterized. Further, there are described all connected monounary algebras (A, f) such that the lattice R∅(A, f) is complemented. In this case R∅(A, f) forms a boolean lattice. monounary algebra (dpeaa)DE-He213 retract (dpeaa)DE-He213 retract lattice (dpeaa)DE-He213 Pócs, Jozef aut Enthalten in Mathematica Slovaca Warsaw : Versita, 2007 62(2012), 2 vom: 29. Feb., Seite 169-186 (DE-627)548127344 (DE-600)2393408-6 1337-2211 nnns volume:62 year:2012 number:2 day:29 month:02 pages:169-186 https://dx.doi.org/10.2478/s12175-012-0002-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 62 2012 2 29 02 169-186
allfieldsSound	10.2478/s12175-012-0002-4 doi (DE-627)SPR02542744X (SPR)s12175-012-0002-4-e DE-627 ger DE-627 rakwb eng Jakubíková-Studenovská, Danica verfasserin aut Some properties of retract lattices of monounary algebras 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © © Versita Warsaw and Springer-Verlag Wien 2012 Abstract Necessary and sufficient conditions for a connected monounary algebra (A, f), under which the lattice R∅(A, f) of all retracts of (A, f) (together with ∅) is algebraic, are proved. Simultaneously, all connected monounary algebras in which each retract is a union of completely join-irreducible elements of R∅(A, f) are characterized. Further, there are described all connected monounary algebras (A, f) such that the lattice R∅(A, f) is complemented. In this case R∅(A, f) forms a boolean lattice. monounary algebra (dpeaa)DE-He213 retract (dpeaa)DE-He213 retract lattice (dpeaa)DE-He213 Pócs, Jozef aut Enthalten in Mathematica Slovaca Warsaw : Versita, 2007 62(2012), 2 vom: 29. Feb., Seite 169-186 (DE-627)548127344 (DE-600)2393408-6 1337-2211 nnns volume:62 year:2012 number:2 day:29 month:02 pages:169-186 https://dx.doi.org/10.2478/s12175-012-0002-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 62 2012 2 29 02 169-186
language	English
source	Enthalten in Mathematica Slovaca 62(2012), 2 vom: 29. Feb., Seite 169-186 volume:62 year:2012 number:2 day:29 month:02 pages:169-186
sourceStr	Enthalten in Mathematica Slovaca 62(2012), 2 vom: 29. Feb., Seite 169-186 volume:62 year:2012 number:2 day:29 month:02 pages:169-186
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author	Jakubíková-Studenovská, Danica
spellingShingle	Jakubíková-Studenovská, Danica misc monounary algebra misc retract misc retract lattice Some properties of retract lattices of monounary algebras
authorStr	Jakubíková-Studenovská, Danica
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topic_title	Some properties of retract lattices of monounary algebras monounary algebra (dpeaa)DE-He213 retract (dpeaa)DE-He213 retract lattice (dpeaa)DE-He213
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title	Some properties of retract lattices of monounary algebras
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title_full	Some properties of retract lattices of monounary algebras
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doi_str_mv	10.2478/s12175-012-0002-4
title_sort	some properties of retract lattices of monounary algebras
title_auth	Some properties of retract lattices of monounary algebras
abstract	Abstract Necessary and sufficient conditions for a connected monounary algebra (A, f), under which the lattice R∅(A, f) of all retracts of (A, f) (together with ∅) is algebraic, are proved. Simultaneously, all connected monounary algebras in which each retract is a union of completely join-irreducible elements of R∅(A, f) are characterized. Further, there are described all connected monounary algebras (A, f) such that the lattice R∅(A, f) is complemented. In this case R∅(A, f) forms a boolean lattice. © © Versita Warsaw and Springer-Verlag Wien 2012
abstractGer	Abstract Necessary and sufficient conditions for a connected monounary algebra (A, f), under which the lattice R∅(A, f) of all retracts of (A, f) (together with ∅) is algebraic, are proved. Simultaneously, all connected monounary algebras in which each retract is a union of completely join-irreducible elements of R∅(A, f) are characterized. Further, there are described all connected monounary algebras (A, f) such that the lattice R∅(A, f) is complemented. In this case R∅(A, f) forms a boolean lattice. © © Versita Warsaw and Springer-Verlag Wien 2012
abstract_unstemmed	Abstract Necessary and sufficient conditions for a connected monounary algebra (A, f), under which the lattice R∅(A, f) of all retracts of (A, f) (together with ∅) is algebraic, are proved. Simultaneously, all connected monounary algebras in which each retract is a union of completely join-irreducible elements of R∅(A, f) are characterized. Further, there are described all connected monounary algebras (A, f) such that the lattice R∅(A, f) is complemented. In this case R∅(A, f) forms a boolean lattice. © © Versita Warsaw and Springer-Verlag Wien 2012
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title_short	Some properties of retract lattices of monounary algebras
url	https://dx.doi.org/10.2478/s12175-012-0002-4
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Some properties of retract lattices of monounary algebras

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