Products of idempotent matrices over integral domains

We say that a ring R has the idempotent matrices property if every square singular matrix over R is a product of idempotent matrices. It is known that every field, and more generally, every Euclidean domain has the idempotent matrices property. In this paper we show that not every integral domain has the idempotent matrices property and that if a projective free ring has the idempotent matrices property then it must be a Bezout domain. We also show that a principal ideal domain has the idempotent matrices property if and only if every fraction a/b with b not equal 0 has a finite continued fraction expansion. New proofs are also provided for the results that every field and every Euclidean domain have the idempotent matrices property. (C) 2008 Elsevier Inc. All rights reserved.