π-群强半格的同余

Congruence on a strong semilattice of π-groups

一个半群是Clifford半群当且仅当它是群的强半格,π-群是群在π-正则半群范围内的推广.同余是研究半群性质和结构的重要手段和工具.研究了π-群的强半格上的正则同余,并给出了π-群强半格上的同余是正则同余的充要条件.

It is well known that a semigroup is a Clifford semigroup,if and only if it is a strong semilattice of groups,and the class ofπ-groups is the generalization of groups in the range ofπ-regular semigroups.Congruence is an important tool when studying the characterization and structure of a semigroup.In this paper,we consider the regular congruences on a strong semilattice ofπ-groups,and give necessary and sufficient conditions for a congruence on a strong semilattice ofπ-groups to be a regular congruence.