PRODUCTS OF IDEMPOTENT ENDOMORPHISMS OF FREE ACTS OF INFINITE RANK

In 1966, J. M. Howie characterized the self-maps of a set which can be written as a product (i.e., composite) of idempotent self-maps of tha t set. Using a wreath product construction introduced by V. Fleischer, the first-named author was recently able to describe products of idem potent endomorphisms of a free S-act of finite rank where S is any mon oid. The purpose of the present paper is to extend this result to free S-acts of infinite rank.