STRUCTURE AND SOME CHARACTERIZATIONS OF LEFT k-CLIFFORD SEMIRINGS

Abstract

Here, being motivated from the works of Zhu, Guo and Shum on left Clifford semigroups, we have introduced left k-Clifford semirings as a generalization of k-Clifford semirings. A k-regular semiring S ∈ 𝕊𝕃+ is a left k-Clifford semiring (left k-semifield) if for all a ∈ S, [Formula: see text] (for all b ∈ S′, [Formula: see text]). Several characteristics for this class of semirings are obtained. Moreover a semiring is left k-Clifford if and only if it is a distributive lattice of left k-semifields.