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Different Types of Prime bi-ideals in Ternary Semirings

Kings Engineering College, Department of Mathematics, Chennai, 602117, India.

Bharath Institute of Higher Education and Research, Department of Mathematics, Chennai, 600073, India

* Corresponding Author
Annals of Communications in Mathematics 2021
, 4 (2),
141-148.
https://doi.org/10.62072/acm.2021.040206
Received: 21 April 2021 |
Accepted: 15 June 2021 |
Published: 30 September 2021

Abstract

To interact three different types of prime bi-ideals are introduce and the relation between them is obtain. Also we have define three different mb -systems. The bi-ideal P of a ternary semiring R is 2-prime if and only if RML ⊆ P, where R is a right ideal, M is a lateral ideal and L is a left ideal of R, implies R ⊆ P or M ⊆ P or L ⊆ P. If B is a bi-ideal of R, then HB is the unique largest two-sided ideal of R contained B. Let M be a mb 3 system and bi-ideal B of R with B ∩ M = φ. Then there exists a 3-prime P of R containing B with P ∩ M = φ.

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Cite This Article

Different Types of Prime bi-ideals in Ternary Semirings.

Annals of Communications in Mathematics,

2021,
4 (2):
141-148.
https://doi.org/10.62072/acm.2021.040206
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  • Copyright (c) 2023 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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