Factorization in the semigroup generated by the idempotents of the semigroup of full contractions of a finite chain

Abstract

Let [n] = {1, 2, . . . , n} be a finite chain and let CT n be the semigroup of full contractions on [n]. It was shown in [3] that the semigroup generated by idempotents is a regular semigroup (denoted by 〈E(CT n)〉). In this paper, we investigate factorization properties in this semigroup.