NEC rings

Abstract

A ring R is called NEC if for any a, b ∈ N(R), ab = ba. The class of NEC rings is a proper generalization of the class of CN rings. First, with the aid of NEC rings, some characterizations of CN rings and reduced rings are given. Next we extend many properties of CN rings to NEC rings such as we show that NEC rings are directly finite and left min-abel; NEC regular ring are strongly regular ; a ring R is NEC if and only if every Pierce stalk of R is NEC; Also we discuss some properties of NEC exchange rings; Finally, we give some properities of MP-invertible elements. 2010 Mathematics Subject Classification. 16E50 16D30 16B99 Keywords. NEC ring; reduced ring; clean ring; exchange ring; quasi-normal ring; regular ring; Moore penrose inverse; EP element.