A morphic ring of neat range one

Abstract

We show that a commutative ring R has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring R has a neat range one if and only if for any elements a,b ∈ R such that aR=bR there exist neat elements s,t∈R such that bs=c, ct=b. Examples of morphic rings of neat range one are given.