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Authors:
Title:
On 3-prime and quasi 3-primary ideals of ternary semirings
PDFSource:
Discussiones Mathematicae - General Algebra and Applications
Received: 2021-12-31 , Revised: 2023-01-11 , Accepted: 2022-01-11 , Available online: 2024-03-25 , https://doi.org/10.7151/dmgaa.1434
Abstract:
The purpose of this paper is to introduce the concept of 3-prime ideal as a
generalization of prime ideal. Further, we generalize the concepts of 3-prime
ideal and primary ideal, namely as quasi 3-primary ideal in a commutative
ternary semiring with zero. The relationship among prime ideal, 3-prime ideal,
primary ideal, quasi primary and quasi 3-primary ideal are investigated.
Various results and examples concerning 3-prime ideals and quasi 3-primary
ideals are given. Analogous theorems to the primary avoidance theorem for quasi
3-primary ideals are also studied.
Keywords:
ternary semiring, regular ternary semiring, 3-prime ideals, quasi 3-primary ideals
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