The characterization of regular hemirings.
type: Item
instance of: scholarly article
title: The characterization of regular hemirings.
zbMATH Open document ID: 1189.16039
author: Hongjie Li
author: Xiaokun Huang
author: Yunqiang Yin
published in: Southeast Asian Bulletin of Mathematics
publication date: 2010-02-12T00:00:00Z
review text: A hemiring is an algebra \((S,+,\cdot)\) which has all the properties of a ring except that \((S,+)\) is a commutative semigroup (with zero) rather than a commutative group. A left ideal \(A\) of a hemiring \(S\) is called left \(h\)-ideal if for \(\forall x,z\in S\), \(\forall a,b\in A\) from \(x+a+z=b+z\) follows \(x\in A\). A fuzzy subset \(\mu\colon S\to [0,1]\) of a hemiring \(S\) is called fuzzy \(h\)-bi-ideal if for \(\forall x,y,z,a,b\in S\) holds \(\mu(x+y)\geq\min(\mu(x),\mu(y))\), \(\mu(xy)\geq\min(\mu(x),\mu(y))\), \(\mu(xyz)\geq\min(\mu(x),\mu(z))\) and \(x+a+z=b+z\Rightarrow\mu(x)\geq\min(\mu(a),\mu(b))\). A hemiring \(S\) is called \(h\)-hemiregular if \((\forall x\in S)(\exists a,a',z\in S)(x+xax+z=xa'x+z)\). Here are investigated properties of fuzzy \(h\)-bi-ideals, fuzzy \(h\)-quasi-ideals and \(h\)-hemiregular hemirings; the paper contains some misprints.
Mathematics Subject Classification ID: 16Y60
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 20N25
zbMATH DE Number: 5669439
zbMATH Keywords: fuzzy bi-ideals
zbMATH Keywords: fuzzy quasi-ideals
zbMATH Keywords: fuzzy ideals
zbMATH Keywords: hemiregular hemirings
reviewed by: Jaak Henno
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5669439