Article in press
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
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 be a multiplicatively closed subset of R. Hamed and Malek[7] defined an ideal P of R disjoint with S to be S−prime ideal if for any a, b ∈ R with ab ∈ P implies that there exists s ∈ S such that sa ∈ P or sb ∈ 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
References:
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