• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2022, Volume: 15, Issue: 39, Pages: 2037-2040

Original Article

Prime Quasi-Ideals in Ternary Seminear Rings

Received Date:18 August 2022, Accepted Date:19 September 2022, Published Date:17 October 2022


Objectives/Background: The ternary seminear ring is the generalization of seminear ring and it need not be a ternary semiring. Characterization of quotient ternary seminear rings and some structures of ternary seminear ring have been analysed and also studied ideals in ternary seminear rings. Further quasi ideals in ternary seminear rings defined and discussed about their properties. Methods: Properties of seminear ring and ternary semiring have been employed to carry out this research work to obtain all the characterizations of ternary seminear rings corresponding to that ternary semiring. Findings: We call an algebraic structure (T;+; :) is a ternary seminear ring if (T,+) is a Semigroup, T is a ternary semigroup under ternary multiplication and xy(z+u) = xyx+xyu for all x;y; z;u 2 T. T is said to have an absorbing zero if there exists an element 0 2 T such that x+0 = 0+x = x for all x 2 T and xy0 = x0y = 0xy = 0 for all x;y 2 T. Throughout this paper T will always stand for ternary seminear ring with an absorbing zero. In this ternary structure we try to study prime quasi ideals concept and obtain their properties. Novelty: In this study, we define the notion of Prime quasi ideals in ternary seminear rings. We also find some of their interesting results. AMS Subject Classification code: 16Y30,16Y99,17A40

Keywords: Ternary seminear ring; Idempotent ternary seminear ring; Ideals in ternary seminear ring; Quasi Ideals in ternary seminear ring; Prime Ideals in ternary seminear rings.


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© 2022 Vijayakumar & Bharathi. 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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