Some notes on nil-semicommutative rings
Authors : Yinchun Qu, Junchao Wei
Pages : 212-224
Doi:10.3906/mat-1202-44
View : 10 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :A ring R is defined to be nil-semicommutative if ab \in N(R) implies arb \in N(R) for a, b, r \in R, where N(R) stands for the set of nilpotents of R. Nil-semicommutative rings are generalization of NI rings. It is proved that (1) R is strongly regular if and only if R is von Neumann regular and nil-semicommutative; (2) Exchange nil-semicommutative rings are clean and have stable range 1; (3) If R is a nil-semicommutative right MC2 ring whose simple singular right modules are YJ-injective, then R is a reduced weakly regular ring; (4) Let R be a nil-semicommutative p-regular ring. Then R is an (S, 2)-ring if and only if Z/2 Z is not a homomorphic image of R.Keywords : Nil-semicommutative rings, clean rings, von Neumann regular rings, (S, 2)-rings