Kernel normal systems for a semigroup.
type: Item
instance of: scholarly article
title: Kernel normal systems for a semigroup.
zbMATH Open document ID: 1123.20051
author: N. E. Zubov
published in: Southeast Asian Bulletin of Mathematics
publication date: 2007-04-10T00:00:00Z
review text: The authors define a kernel normal system in a semigroup \(S\) to be the set of all idempotent congruence classes of some congruence on \(S\). It has long been known that on regular semigroups, each congruence is determined by its associated kernel normal system. Clearly, that need not be true in general, since for any congruence for which the quotient semigroup is idempotent-free, the kernel normal system will be empty. It is shown that every kernel normal system corresponds to an interval of congruences on \(S\). If \(\rho\) is a regular congruence on \(S\) (in the sense that \(S/\rho\) is a regular semigroup) then it is the greatest member of that interval. Hence regular congruences on \(S\) are determined by their kernel normal systems. The authors go on to consider the lattice of kernel normal systems and its relationship to the lattice of congruences.
reviewed by: Peter R. Jones
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 5141237
zbMATH Keywords: admissible systems
zbMATH Keywords: idempotent congruence classes
zbMATH Keywords: intervals of congruences
zbMATH Keywords: regular congruences
zbMATH Keywords: lattices of kernel normal systems
zbMATH Keywords: lattices of congruences
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5141237