Some remarks on semirings and their ideals

TL;DR

This paper explores semiring analogues of classical algebraic structures like Euclidean rings, PIDs, and UFDs, extending fundamental algebraic concepts to the semiring context.

Contribution

It provides semiring versions of key results in commutative algebra, bridging classical theory and semiring structures.

Findings

Semiring analogues of Euclidean rings and PIDs established

Characterization of G-domains and GCD properties in semirings

Extension of integrally closed domain concepts to semirings

Abstract

In this paper, we give semiring version of some classical results in commutative algebra related to Euclidean rings, PIDs, UFDs, G-domains, and GCD and integrally closed domains.