"ON CLEAN FREE MODULES AND A CHARACTERIZATION OF CLEAN RINGS"

Abstract

"In this paper, the concept of clean ring is generalized to modules. We call a free R-module, Rn, clean, whenever every element of Rn can be written as the sum of a unimodular and an idempotent row. We show that when R is Noetherian, the R-module Rn is clean if and only if R can be expressed as a finite direct product of indecomposable rings Ri, say R = Lt i=1 Ri, such that each Ri has at most 2n − 1 maximal ideals. We also give a new characterization of clean rings."