On \(k\)-ideals of semirings
type: Item
instance of: scholarly article
title: On \(k\)-ideals of semirings
zbMATH Open document ID: 0779.16020
DOI: 10.1155/S0161171292000437
author: M. K. Sen
author: M. R. Adhikari
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1992-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/46891
review text: The paper deals with semirings \(S=(S,+,\cdot)\) such that \((S,+)\) is a commutative inverse semigroup. It contains two results: (1) Each congruence \(\rho\) on \(S\) such that \(S\rho\) is a ring satisfies \(\rho=\{(x,y)\mid x+a_ 1=y+ a_ 2\) for some \(a_ i\in A\}\), where \(A\) is a \(k\)-ideal of \(S\) containing the set \(E^ +\) of idempotents of \((S,+)\), and conversely. [This was already proved by the same authors in Algebra and number theory, Proc. Symp., Kochi/India 1990, Publ., Cent. Math. Sci., Trivandrum 20, 85-89 (1990), cf. the remarks in the review Zbl 0754.16024.] (2) The \(k\)-ideals \(A\) of \(S\) satisfying \(E^ +\subseteq A\) form a complete modular lattice. [This would be a consequence of Theorem 4.1 in the paper cited above, however, this theorem fails to be true which was overlooked by the referee at that time].
reviewed by: Hanns Joachim Weinert
Mathematics Subject Classification ID: 16Y60
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 39593
zbMATH Keywords: semirings
zbMATH Keywords: inverse semigroup
zbMATH Keywords: congruence
zbMATH Keywords: idempotents
zbMATH Keywords: \(k\)-ideals
zbMATH Keywords: complete modular lattice
MaRDI profile type: Publication
OpenAlex ID: W2009291268
description: scientific article; zbMATH DE number 39593