k-prime and k-semiprime ideals of semirings

Abstract

In this paper, we study the notions of [Formula: see text]-prime and [Formula: see text]-semiprime ideals of semirings, [Formula: see text]-[Formula: see text]-system and [Formula: see text]-[Formula: see text]-system. We produce some properties and characterizations for [Formula: see text]-prime and [Formula: see text]-semiprime ideals of semirings in terms of [Formula: see text]-[Formula: see text]-system and [Formula: see text]-[Formula: see text]-system, respectively. We initiate the notion of prime semiring and semiprime semiring to set up characterizations for these two ideals of a semiring. The concept of power semiring associated to a semigroup is also studied in this paper.