Congruences on *-Regular Semigroups

Siniša Crvenković; Igor Dolinka

doi:10.1023/a:1022355610931

Jump to Content

Periodica Mathematica Hungarica

Volume/Issue:: Volume 45: Issue 1-2

Congruences on *-Regular Semigroups

Authors:

Siniša Crvenković

Siniša Crvenković University of Novi Sad Department of Mathematics and Computing Trg D. Obradovića 4 21000 Novi Sad Yugoslavia

Search for other papers by Siniša Crvenković in
Current site
Google Scholar
PubMed

and

Igor Dolinka

Igor Dolinka University of Novi Sad Department of Mathematics and Computing Trg D. Obradovića 4 21000 Novi Sad Yugoslavia

Search for other papers by Igor Dolinka in
Current site
Google Scholar
PubMed

View More View Less

Pages:: 1–13

Online Publication Date:: 03 Jan 2005

Publication Date:: 01 Sep 2002

Article Category:: Research Article

DOI:: https://doi.org/10.1023/a:1022355610931

Keywords:: *-regular semigroup; *-kernel; congruence; *-trace

Restricted access

Abstract

In this paper we study the congruences of *-regular semigroups, involution semigroups in which every element is p-related to a projection (an idempotent fixed by the involution). The class of *-regular semigroups was introduced by Drazin in 1979, as the involutorial counterpart of regular semigroups. In the standard approach to *-regular semigroup congruences, one ,starts with idempotents, i.e. with traces and kernels in the underlying regular semigroup, builds congruences of that semigroup, and filters those congruences which preserve the involution. Our approach, however, is more evenhanded with respect to the fundamental operations of *-regular semigroups. We show that idempotents can be replaced by projections when one passes from regular to *-regular semigroup congruences. Following the trace-kernel balanced view of Pastijn and Petrich, we prove that an appropriate equivalence on the set of projections (the *-trace) and the set of all elements equivalent to projections (the *-kernel) fully suffice to reconstruct an (involution-preserving) congruence of a *-regular semigroup. Also, we obtain some conclusions about the lattice of congruences of a *-regular semigroup.

Save
Cite
Email this content

Share Link

Copy this link, or click below to email it to a friend
Email this content
or copy the link directly:

https://akjournals.com/abstract/journals/10998/45/1-2/article-p1.xml
The link was not copied. Your current browser may not support copying via this button.

Link copied successfully

Collapse
Expand

Periodica Mathematica Hungarica

Print ISSN:: 0031-5303

Online ISSN:: 1588-2829

To see the editorial board, please visit the website of Springer Nature.

Manuscript Submission: HERE

For subscription options, please visit the website of Springer Nature.

Periodica Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1971
Volumes per Year	2
Issues per Year	4
Founder	Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's Address	H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0031-5303 (Print)
ISSN	1588-2829 (Online)