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Generalized fine rings.
- Source :
- Journal of Algebra & Its Applications; Mar2022, Vol. 21 Issue 3, p1-9, 9p
- Publication Year :
- 2022
-
Abstract
- As introduced by Cǎlugǎreanu and Lam in [G. Cǎlugǎreanu and T. Y. Lam, Fine rings: a new class of simple rings, J. Algebra Appl.15(9) (2016) 1650173, 18 pp.], a fine ring is a ring whose every nonzero element is the sum of a unit and a nilpotent. As a natural generalization of fine rings, a ring is called a generalized fine ring if every element not in the Jacobson radical is the sum of a unit and a nilpotent. Here some known results on fine rings are extended to generalized fine rings. A notable result states that matrix rings over generalized fine rings are generalized fine, extending the important result in [G. Cǎlugǎreanu and T. Y. Lam, Fine rings: a new class of simple rings, J. Algebra Appl.15(9) (2016) 1650173, 18 pp.] that matrix rings over fine rings are fine. [ABSTRACT FROM AUTHOR]
- Subjects :
- JACOBSON radical
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 21
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 155687672
- Full Text :
- https://doi.org/10.1142/S0219498822500608