On the Primary Decomposition of k-Ideals and Fuzzy k-Ideals in Semirings

Abstract

Observing that every k-irreducible ideal of a semiring R is a k-primary ideal, if R is an additively cancellative, yoked and commutative Noetherian semiring, we establish the primary decomposition and uniqueness of the primary decomposition of k-ideals of such semirings. Finally, the primary decomposition and uniqueness of primary decomposition proved for k-ideals is also generalised for fuzzy k-ideals of these semirings.