Article in volume
Authors:
Sumon Bhowmick
Department of Mathematics
Gauhati University
Guwahati-14, Assam, India
email: sumonbhowmick31@gmail.com
Sukhendu Kar
Department of Mathematics
Jadavpur University
Kolkata-32, West Bengal, India
email: karsukhendu@yahoo-co.in
Title:
$S$−$k$−prime and $S$−$k$−semiprime ideals of semirings
PDFSource:
Discussiones Mathematicae - General Algebra and Applications 44(2) (2024) 301-317
Received: 2022-08-04 , Revised: 2023-05-11 , Accepted: 2023-05-11 , Available online: 2023-09-01 , https://doi.org/10.7151/dmgaa.1442
Abstract:
Let $R$ be a commutative ring and $S$ a multiplicatively closed subset of $R$.
Hamed and Malek [7] defined an ideal $P$ of $R$ disjoint with $S$
to be an $S$-prime ideal of $R$ if there exists an $s \in S$ such that for all
$a, b \in R$ if $ab \in P$, then $sa \in P$ or $sb \in P$. In this paper, we
introduce the notions of $S$-$k$-prime and $S$-$k$-semiprime ideals of
semirings, $S$-$k$-$m$-system, and $S$-$k$-$p$-system. We study some properties
and characterizations for $S$-$k$-prime and $S$-$k$-semiprime ideals of
semirings in terms of $S$-$k$-$m$-system and $S$-$k$-$p$-system respectively.
We also introduce the concepts of $S$-prime semiring and $S$-semiprime semiring
and study the characterizations for $S$-$k$-prime and $S$-$k$-semiprime ideals
in these two semirings.
Primary keywords:
Semiring, $S$−$k$prime ideal, $S$−$k$−semiprime ideal
Secondary keywords:
$S$−prime semiring, $S$−semiprime semiring
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