PRODUCTS OF IDEMPOTENT ENDOMORPHISMS OF AN INDEPENDENCE ALGEBRA OF INFINITE RANK

In 1966, J.M. Howie characterized the self-maps of a set which can be written as a product (under composition) of idempotent self-maps of th e same set. In 1967, J. A. Erdos considered the analogous question for linear maps of a finite dimensional vector space and in 1985, Reynold s and Sullivan solved the problem for linear maps of an infinite dimen sional vector space. Using the concept of independence algebra, the au thors gave a common generalization of the results of Howie and Erdos f or the cases of finite sets and finite dimensional vector spaces. In t he present paper we introduce strong independence algebras and provide a common generalization of the results of Howie and Reynolds and Sull ivan for the cases of infinite sets and infinite dimensional vector sp aces.