具有中心幂等元的(L)-弱正则半群

摘要

Weakly L-regular semigroups with central idempotents are introduced and their algebraic structures are studied in this paper. By using a right congruence L+ and a left congruence R+ on a semigroup S, respectively, we show that a semigroup S is a weakly L-regular semigroup with central idempotents if and only if S is a strong semilattice of H~left cancellative monoids, which generalizes the corresponding results of Clifford semigroups in the class of regular semigroups.%本文定义了具有中心幂等元的(L)-弱正则半群,研究了这类半群的代数结构.利用半群上的右同余(L)+和左同余R+,证明了半群S是一个具有中心幂等元的(L)-弱正则半群,当且仅当S是H-左可消幺半群的强半格.这推广了Clifford半群的相应结果.