科研之友
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摘要
Let S be a regular semigroup and (E) over bar be the subsemigroup of S generated by the set E of all idempotent elements of S. By [1], an idempotent element u of S is called a normal idempotent if xux = x for every x is an element of (E) over bar and u (E) over baru is a semilattice. In this paper we introduce the notion of a quasi-normal idempotent of S as an idempotent element u of S which satisfies the conditions: eue = e for every e is an element of (E) over bar and u (E) over baru is a semilattice. It is clear that every normal idempotent is quasi-normal. The main purpose of our paper is to show the converse statement, that is, every quasi-normal idempotent of a regular semigroup is also normal.
