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, 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.
generalization of the class of CN rings. First, with the aid of NEC, 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.
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