S. Bulmanfleming et J. Fountain, PRODUCTS OF IDEMPOTENT ENDOMORPHISMS OF FREE ACTS OF INFINITE RANK, Monatshefte fuer Mathematik, 124(1), 1997, pp. 1-16
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.