单幂幺半群的半格

On Semilattices of Unipotent Semigroups

给出了单幂幺半群的半格的4条等价刻画.即对于半群S,以下4条刻画等价:ⅰ)S是单幂幺半群的半格;ⅱ)S是单幂幺半群的强半格;ⅲ)S是■-富足的,■为S上的同余,且S是幂等元中心的;ⅳ)S是■-富足的,■为S上的同余,且在S上,■=■.推广了Clifford半群的结构定理.

Four equivalent descriptions have been given for semigroups which are semilattices of unipotent semigroups.Namely,the following conditions on a semigroup S are equivalent： ⅰ） S is a semilattice of unipotent semigroups;ⅱ） S is a strong semilattices of unipotent semigroups;ⅲ） S is central for idempotents and an ■-abundant semigroup on which ■ is a congruence;ⅳ） S is central for idempotents and an ■-abundant semigroup satisfying ■=■.Thus the structure theorem for Clifford semigroups is generalized.