On prime k-ideals in semirings

Abstract

We establish eighteen conditions for $k$-ideals to be prime $k$-ideals in semirings. It has been shown that $0(1-2)$-prime ideals coincide with prime $k$-ideal when the ideal is $k$-ideal. We relate prime $k$-ideal with all $m$-systems. We guarantee the existence of prime $k$-ideal which contains given $k$-ideal that does not intersect given $m_2(m_0,m_1)$-system.