Some notes on nil-semicommutative rings

Authors : Yinchun QU, Junchao WEI

Pages : 212-224

Doi:10.3906/mat-1202-44

View : 15 | Download : 6

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :A ring R is defined to be nil-semicommutative if ab \in Ninsert ignore into journalissuearticles values(R); implies arb \in Ninsert ignore into journalissuearticles values(R); for a, b, r \in R, where Ninsert ignore into journalissuearticles values(R); stands for the set of nilpotents of R. Nil-semicommutative rings are generalization of NI rings. It is proved that insert ignore into journalissuearticles values(1); R is strongly regular if and only if R is von Neumann regular and nil-semicommutative; insert ignore into journalissuearticles values(2); Exchange nil-semicommutative rings are clean and have stable range 1; insert ignore into journalissuearticles values(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; insert ignore into journalissuearticles values(4); Let R be a nil-semicommutative p-regular ring. Then R is an insert ignore into journalissuearticles values(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