\({\mathcal K}G\)-strong semilattice structure of regular orthocryptosemigroups.
type: Item
instance of: scholarly article
title: \({\mathcal K}G\)-strong semilattice structure of regular orthocryptosemigroups.
zbMATH Open document ID: 1114.20044
author: Zhiling Yuan
author: Xiangzhi Kong
published in: Semigroup Forum
publication date: 2007-01-24T00:00:00Z
review text: A semigroup \(S\) is called 1) `semisuperabundant' if each of its \(\widetilde{\mathcal H}\)-classes contains an idempotent, where \(\widetilde{\mathcal H}\) is Green's \(\sim\)-relation; 2) `orthosemigroup' if \(E(S)\) is a subsemigroup of \(S\); 3) `cryptosemigroup' if \(\widetilde{\mathcal H}\) is a congruence; 4) `u-semigroup' if \(S\) has a unique idempotent, which is its identity. The authors introduce the concept of \(\widetilde{\mathcal K}G\)-strong semilattice decomposition of a semigroup \(S\) where \(\widetilde{\mathcal K}\) is an equivalence relation on a semilattice decomposition of \(S\). Let \(S\) be a semisuperabundant orthosemigroup. Then: 1) \(S\) is a regular orthocryptosemigroup if and only if \(S\) is an \(\widetilde{\mathcal H}G\)-strong semilattice of rectangular u-semigroups; 2) \(S\) is a quasinormal orthocryptosemigroup if and only if \(S\) is an \(\widetilde{\mathcal L}G\)-strong semilattice of rectangular u-semigroups; 3) \(S\) is a normal orthocryptosemigroup if and only if \(S\) is a \(\widetilde{\mathcal J}G\)-strong semilattice of rectangular u-semigroups.
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 5118110
zbMATH Keywords: regular orthocryptosemigroups
zbMATH Keywords: \({\mathcal K}G\)-strong semilattices
zbMATH Keywords: natural partial order
zbMATH Keywords: idempotents
zbMATH Keywords: Green relations
zbMATH Keywords: congruences
zbMATH Keywords: u-semigroups
zbMATH Keywords: strong semilattice decompositions
reviewed by: Peeter Normak
MaRDI profile type: Publication
full work available at URL: s00233-006-0614-5
OpenAlex ID: W1969668519
DOI: 10.1007/S00233-006-0614-5
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description: scientific article; zbMATH DE number 5118110