Turkish Journal of Mathematics
DOI
10.3906/mat-1109-1
Abstract
A ring R is called NZI if for any a \in R, l(a) is an N-ideal of R. In this paper, we first study some basic properties and basic extensions of NZI rings. Next, we study the strong regularity of NZI rings and obtain the following results: (1) Let R be a left SF-ring. Then R is a strongly regular ring if and only if R is an NZI ring; (2) If R is an NZI left MC2 ring and every simple singular left R-module is nil-injective, then R is reduced; (3) Let R be an NZI ring. Then R is a strongly regular ring if and only if R is a von Neumann regular ring; (4) Let R be an NZI ring. Then R is a clean ring if and only if R is an exchange ring.
Keywords
Reduced ring, SF ring, strongly regular ring, N-ideal, NZI ring, nil-injective
First Page
781
Last Page
792
Recommended Citation
WANG, LONG; WEI, JUNCHAO; and LI, LIBIN
(2013)
"NZI rings,"
Turkish Journal of Mathematics: Vol. 37:
No.
5, Article 6.
https://doi.org/10.3906/mat-1109-1
Available at:
https://journals.tubitak.gov.tr/math/vol37/iss5/6
