Geodesic
On 3-prime and quasi 3-primary ideals of ternary semirings
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 163-175

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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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Mandal, Manasi; Tamang, Nita; Das, Sampad. On 3-prime and quasi 3-primary ideals of ternary semirings. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 163-175. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_1_a10/