Factorizations of Matrices over Projective-free Rings

Abstract

An element of a ring R is called strongly J(#)-clean provided that it can be written as the sum of an idempotent and an element in J(#)(R) that commute. In this paper, we characterize the strong J(#)-cleanness of matrices over projective-free rings. This extends many known results on strongly clean matrices over commutative local rings.