On w-Neat Rings‎

Abstract

‎In this paper‎, ‎we offer a new generalization of the neat ring that is called a w-neat ring‎. ‎A ring $ R $ is said to be weakly clean if every $ r\in R $ can be written as $ r=u+e $ or $ r=u-e $ where $ u\in‎$ U$(R) $ and $ e\in‎$ I‎‏d$‎(R) $‎. ‎We define a w-neat ring to be one for which every proper homomorphic image is weakly clean‎.‎We obtain some properties of w-neat rings‎.

Keywords

• ‎clean ring‎
• ‎cleaned poorly ring‎
• w-neat ring