Prime Fuzzy Ideals of a Gamma Semiring -1

Tilak Raj Sharma; Ritu Sharma

doi:10.17485/IJST/v16i31.1333

Article

Prime Fuzzy Ideals of a Gamma Semiring -1

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i31.1333

Year: 2023, Volume: 16, Issue: 31, Pages: 2441-2446

Original Article

Prime Fuzzy Ideals of a Gamma Semiring -1

Tilak Raj Sharma^1*, Ritu Sharma²

¹Department of Mathematics, Himachal Pradesh University, Regional Centre, Khaniyara Dharamshala, 176218, Himachal Pradesh, India
²Department of Mathematics, Government College Mandi, Himachal Pradesh, India

*Corresponding Author
Email: [email protected]

Received Date:01 June 2023, Accepted Date:01 June 2023, Published Date:18 August 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: The main objective of this article is to introduce some fundamental results of fuzzy ideals and Prime fuzzy ideals of a G􀀀 semiring R . Methods: We use some fundamental results of fuzzy ideals and conditions like semi subtractive, centreless etc. for developments of the main results. Findings: In this connection, we establish some important results of fuzzy ideals and prime fuzzy ideals of semirings to G􀀀 semirings. Novelty: We find a special class of fuzzy ideals of a G􀀀 semiring R and with this, construct a lattice ordered G􀀀 semiring. Further, we find that a fuzzy ideal of G􀀀 semiring R can be a decreasing map from [0, 1] into the set of R together with an empty set. As an application of this result, the prime fuzzy ideals of a G􀀀semiring R are described in terms of prime ideals of a G􀀀 semiring R.

Keywords: Fuzzy Ideals; Prime Ideals; Prime Fuzzy Ideals; Lattice Ordered G- Semiring; Strong Ideal

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Copyright

© 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)