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. We characterize, in this article, the strongly $J^{#}$-cleanness of matrices over projective-free rings. These extend many known results on strongly clean matrices over commutative local rings.