Turkish Journal of Mathematics
DOI
10.3906/mat-1202-44
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 \pi-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
First Page
212
Last Page
224
Recommended Citation
QU, YINCHUN and WEI, JUNCHAO
(2014)
"Some notes on nil-semicommutative rings,"
Turkish Journal of Mathematics: Vol. 38:
No.
2, Article 3.
https://doi.org/10.3906/mat-1202-44
Available at:
https://journals.tubitak.gov.tr/math/vol38/iss2/3
