• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2023, Volume: 16, Issue: 31, Pages: 2425-2430

Original Article

k-Irreducible Ideals, Common Right Divisors and Euclidean Norms in Gamma Semirings

Received Date:01 June 2023, Accepted Date:08 July 2023, Published Date:16 August 2023


Objectives: The main objective of this paper is to derive some of the results of k􀀀irreducible ideals, common right divisors and Euclidean G 􀀀 semiring: Methods: To establish the main results in G 􀀀 semirings, we use some conditions like commutativity, simple, semi subtractive, centreless, multiplicative G􀀀idempotent, strong multiplicative G􀀀idempotent, additively cancellation and the concept of common right divisor and Euclidean norm. Findings: First we study some results regarding k􀀀irreducible ideals and define a a􀀀 generated ideal by any element of R. In connection with different conditions, we characterize some results of irreducibility in ideals, primary ideals, common right divisors and Euclidean norms. Novelty: Ana􀀀 generated ideal by any element of R, say a, denoted by <aa > is k􀀀ideal if R is simple, semi subtractive and additive cancellative. Again, the conditions mentioned above are used to prove that every k􀀀irreducible ideal of a G􀀀semiring R is primary ideal of R. Furthermore, the concept of Euclidean G􀀀semiring developed to establish various results in the theory of G􀀀semirings.

Keywords: k-Irreducible Ideal; Common Right Divisor; Euclidean Norm; Primary Ideals; Noetherian G-Semirings


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© 2023 Sharma & Sharma. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)


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