Completion of Rectangular Matrices and Power-Free Modules

Abstract. We prove, in this article, that every finitely generated stably free R-module is power-free if and only if for any right invertible rectangular matrix (aij ) over R, there exists s Є N such that (aij Is) can be completed to an invertible matrix. Furthermore, we prove that every right invertible rectangular matrix over generalized stable, right repetitive rings can be completed in this way.