\(\mathcal L\)-subvarieties of the variety of idempotent semirings.
type: Item
instance of: scholarly article
title: \(\mathcal L\)-subvarieties of the variety of idempotent semirings.
zbMATH Open document ID: 1063.08009
DOI: 10.1007/PL00000348
author: Xianzhong Zhao
author: Y. Q. Guo
author: K. P. Shum
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
review text: A semiring \((S;+,\cdot )\) is an algebra of type \((2,2)\) where \((S,+), \, (S,\cdot )\) are semigroups and two distributive identities, \(x\cdot (y+z) = x\cdot y + x\cdot z, \, (x+y)\cdot z = x\cdot z + y\cdot z\), are satisfied. The authors study the Green relations \(\mathcal D\) and \(\mathcal L\) on the semigroups \((S,+), \, (S,\cdot )\) for a semiring \((S;+,\cdot )\). In the case of idempotent semirings, they classify all the varieties where \(\mathcal D\) and/or \(\mathcal L\) for \((S,+)\) and/or \((S,\cdot )\) are congruences or minimal or maximal congruences. They derive equational bases for all of these possibilities.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 16Y60
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 2158733
zbMATH Keywords: idempotent semirings
zbMATH Keywords: Green relations
zbMATH Keywords: varieties
zbMATH Keywords: identities
zbMATH Keywords: congruences
zbMATH Keywords: equational bases
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2158733