Turkish Journal of Mathematics
Article Title
Nilpotent elements and reduced rings
DOI
10.3906/mat-0901-29
Abstract
In this paper, we show the following results: (1) R is a min-leftsemicentral ring if and only if eR(1-e)Re=0 for all e \in ME_l(R); (2) Quasi-normal rings, NI rings and weakly reversible rings are all min-leftsemicentral ring; (3) R is left MC2 ring if and only if aRe=0 implies eRa=0 for all e \in ME_l(R) and a \in R if and only if every projective simple left R-module is MUP-injective; (4) R is reduced if and only if R is n-regular and quasi-normal if and only if R is n-regular and weakly reversible; (5) R is strongly regular if and only if R is regular and quasi-normal if and only if R is regular and weakly reversible.
Keywords
Min-leftsemicentral rings, quasi-normal rings. NCI rings, weakly reversible rings, left MC2 rings, directly finite rings, regular rings
First Page
341
Last Page
353
Recommended Citation
WEI, JUNCHAO and LI, LIBIN
(2011)
"Nilpotent elements and reduced rings,"
Turkish Journal of Mathematics: Vol. 35:
No.
2, Article 15.
https://doi.org/10.3906/mat-0901-29
Available at:
https://journals.tubitak.gov.tr/math/vol35/iss2/15
