Clifford半群的膨胀

引入半群S上的右（左）同余及左（右）平方正则半群，左平方正则半群类在左正则半群类的真推广，证明了半群S是左平方正则半群当且仅当S的每一个L^#-类是S的子半群，同时证明了半群S是群的强半格的膨胀当且仅当S的每一个L^#-类含有一个幕等元，且S的幕等元是中心的。

Inflations of Clifford Semigroups

The right(left) congruence of a semigroup S is introduced, and the left(right) square regular semigroups are introduced. The class of left square regular semigroups is a generalization of the class of left regular semigroups. It is shown that a semigroup S is a left square regular semigroup if and only if each L #-class of S is a subsemigroup of S. Moreover, it is proved that a semigroup S is an inflation of a strong semilattice of groups if and only if each L #-class of S contains an idempotent and the idempotents of S are central.