On an Extension of Green's Relation and a Structure of Semigroup (Languages, Algebra and Computer Systems)
Yukio Kobayashi · Institutional Repositories DataBase (IRDB) · 1999
This paper contains an attempt to discuss some properties of relations induced by transla- tions, including distribution of idempotents.We will begin with start two equivalence relations, give some results to be used frequently and show a distribution of idempotents.In fact it will be shown in " l.Introduction and Preliminaries" that the two relations are relations includingGreen's relations.Using the relations, we will discuss idempotents which behave as left or right identities in equivalence classes induced by the relations.In the last section, as an application of the properties of idempotent and a semigroup extended by translations shown here, some special class of semigroups, abundand semigroups, will be discussed, which is closely related with the distribution of idempotents.