REVIEW ON PRIME IDEALS IN TERNARY SEMIRINGS

Abstract

This article presents a comprehensive analysis of prime ideals in ternary semirings and includes an abstract. Ternary semirings are algebraic structures that can satisfy a set of axioms and come equipped with three different binary operations. In ternary semirings, prime ideals are suitable ideals that have a primeness property associated with them. A comprehensive explanation of ternary semirings, ideals, appropriate ideals, and prime ideals is presented in this article. In addition to this, we talk about the characteristics of prime ideals, such as their radical, prime radical, essential, and maximal features. In addition, we investigate the uses of prime ideals in the research on quotient structures, homomorphisms, and congruences. The results of our research indicate that prime ideals in ternary semirings play an essential part in the algebraic structure of these things. This is demonstrated by the fact that these objects are semirings. We demonstrate that prime ideals can be utilised to describe and organise the many kinds of ternary semirings that are available. The study sheds light on the significance of prime ideals in ternary semirings and the applications of such ideals, providing a clear grasp of both. Keywords: Ternary semirings, ideals, proper ideals, prime ideals, algebraic structures, quotient structures, homomorphisms, and congruences.