Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

CYCLIC ENTROPIC QUASIGROUPS

CYCLIC ENTROPIC QUASIGROUPS DEMONSTRATIO MATHEMATICAVol. XLIINo 22009Grzegorz Binczak*, Joanna KaletaCYCLIC ENTROPIC QUASIGROUPSA b s t r a c t . In this paper we explain the relationship of some entropic quasigroups toabelian groups with involution. It is known t h a t (Zn, —„) are examples of cyclic entropicquasigroups which are not groups. We describe all cyclic entropic quasigroups with quasiidentity.1. IntroductionIn this paper we describe cyclic quasigroups in the variety EQ1. Thisvariety contains abelian groups. The variety of abelian groups is generated byintegers with the usual addition, whereas EQ 1 is generated by two algebras:integers with the usual addition and integers with the usual subtraction.The first section is devoted to the basic definitions. In the second sectionwe show that the variety EQ 1 is equivalent to the variety of abelian groupswith involution. Thanks to this equivalence, dealing with quasigroups inEQ 1 becomes simpler. The notion of rank of an element can be transferedfrom abelian groups to quasigroups in EQ 1. In the third section we describe finite cyclic quasigroups in EQ 1. One can also consider infinite cyclicquasigroups in EQ 1. We deal with this case in the fourth section.Basic information on quasigroups can be found in [2], [5]. In [3] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

CYCLIC ENTROPIC QUASIGROUPS

Bińczak, Grzegorz; Kaleta, Joanna
Demonstratio Mathematica , Volume 42 (2): 14 – Apr 1, 2009
Download PDF
14 pages

Loading next page...
 
/lp/de-gruyter/cyclic-entropic-quasigroups-mu6voHvfRY

References (7)

Publisher
de Gruyter
Copyright
© by Grzegorz Bińczak
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2009-0207
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XLIINo 22009Grzegorz Binczak*, Joanna KaletaCYCLIC ENTROPIC QUASIGROUPSA b s t r a c t . In this paper we explain the relationship of some entropic quasigroups toabelian groups with involution. It is known t h a t (Zn, —„) are examples of cyclic entropicquasigroups which are not groups. We describe all cyclic entropic quasigroups with quasiidentity.1. IntroductionIn this paper we describe cyclic quasigroups in the variety EQ1. Thisvariety contains abelian groups. The variety of abelian groups is generated byintegers with the usual addition, whereas EQ 1 is generated by two algebras:integers with the usual addition and integers with the usual subtraction.The first section is devoted to the basic definitions. In the second sectionwe show that the variety EQ 1 is equivalent to the variety of abelian groupswith involution. Thanks to this equivalence, dealing with quasigroups inEQ 1 becomes simpler. The notion of rank of an element can be transferedfrom abelian groups to quasigroups in EQ 1. In the third section we describe finite cyclic quasigroups in EQ 1. One can also consider infinite cyclicquasigroups in EQ 1. We deal with this case in the fourth section.Basic information on quasigroups can be found in [2], [5]. In [3]

Journal

Demonstratio Mathematica – de Gruyter

Published: Apr 1, 2009

There are no references for this article.