The .°-relation on the congruence lattice of a regular semigroup with an inverse transversal

Authors
Feng, Ying Ying
Citation
Feng, Ying Ying, The .°-relation on the congruence lattice of a regular semigroup with an inverse transversal, Acta mathematica Sinica. English series (Print) , 28(5), 2012, pp. 1061-1074
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
28
Issue
5
Year of publication
2012
Pages
1061 - 1074
Database
ACNP
SICI code
Abstract
Let S be a regular semigroup with an inverse transversal S° and C(S) the congruence lattice of S. A relation .° on C(S) is introduced as follows: if ., . . C(S), then we say that . and . are .°-related if Ker .° = Ker .°, where .° = .|S°. Expressions for the least and the greatest congruences in the same .°-class as . are provided. A number of equivalent conditions for .° being a congruence are given.