Stable range one on non-zero divisors

Abstract

In this paper, almost unit 1-stable range condition for a commutative ring with unity is defined and similar results which are already proved for the weakly unit 1-stable range are proved. Several properties of rings satisfying almost unit 1-stable range are discussed. The characterizations for rings such as presimplifiable semilocal rings and idealization R(M) of a ring R and an R-module M, satisfying almost unit 1-stable range is also given in this paper. Few examples are given to show that almost unit 1-stable range condition is different from other stable range conditions. © 2019, Indian Academy of Sciences.