IDEALS IN SEMIRING WITH INVOLUTION
P. Dheena1, B. Elavarasan2, K. Porselvi2
1Department of Mathematics
Annamalai University
Annamalainagar, 608002, INDIA
2Department of Mathematics
Karunya University
Coimbatore, 641 114, INDIA

Abstract

In this paper, we study the notion of $*$-prime ideal in semiring with involution and shown that if $M$ is a non-void $*$-$m$-system in a semiring with involution and if $I$ is a $*$-ideal of $R$ with $I\cap M=\phi,$ then there exists a $*$-prime ideal $P$ of $R$ such that $I\subseteq P$ and $P\cap M=\phi.$ We also introduce the notion of $*$-$k$-prime ideal and we have shown that if $P$ is a $*$-$k$-ideal of a semiring $R$ with involution, then $P$ is semiprime if and only if $P$ is $*$-$k$-prime.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 3
Year: 2018

DOI: 10.12732/ijam.v31i3.6

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