Idempotent-generated regular semigroups
Carl Eberhart, Wiley Williams, Lael F. Kinch · Journal of the Australian Mathematical Society · 1973
Suppose S is a regular semigroup and E is its set of idempotents. If E is subsemigroup of S, then S has been called orthodox and studied recently by Hall [3], Meakin [6], and Yamada [8]. In this paper we assume that E is not (necessarily) a subsemigroup of S and consider the subsemigroup generated by E, denoted . If E denotes the set of all elements of S which can be written E, denoted . If E denotes the set of all elements of S which can be written as the product of n (not necessarily distinct) idempotents of S, then . We show that is always a regular subsemigroup of S and investigate relationships between it and S. The case where = S is of particular interest to us; such semigroups will be referred to as idempotent-generated regular semi- groups.