Note on idempotent semigroups, II
Miyuki Yamada, Naoki Kimura · Proceedings of the Japan Academy Series A Mathematical Sciences · 1958
the authors 2, and also it is the continuation of the first paper (Kimura [1).Any terminology without definition should be referred to FI].The purpose of this note is to present the structure theorem of normal idempotent semigroups (for the definition, see below)and some relevant matters.2. An idempotent semigroup is called (1) left normal, (2) right normal, (3) normal, respectively, if it satisfies the following correspond- ing identities:1 ) abc--acb, (2) bca=cba,3 ) abca--acba.Now the following lemmas are apparent.Lemma 1.If S is (left, right) normal, then S is (left, right) regular.