Some aspects of $k$-ideals of semirings

The aim of this paper is to study some distinguished classes of $k$-ideals of semirings, which include $k$-prime, $k$-semiprime, $k$-radical, $k$-irreducible, and $k$-strongly irreducible ideals. We discuss some of the properties of $k$-ideals and their products, intersections, and ideal quotients under semiring homomorphisms.