A Note on the Primary Decomposition of k-Ideals in Semirings

TL;DR

This paper explores the primary decomposition of k-ideals in commutative Noetherian semirings, establishing both the existence and uniqueness of such decompositions in this algebraic context.

Contribution

It introduces the primary decomposition theory for k-ideals in semirings and proves the conditions for their uniqueness, extending classical ideal theory.

Findings

Primary decomposition exists for k-ideals in Noetherian semirings.

Uniqueness of primary decomposition is established under certain conditions.

The results generalize classical ideal theory to semirings.

Abstract

We establish the primary decomposition and uniqueness of primary decomposition for k-ideals in commutative Noetherian semirings.