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Reversibility of Rings with Respect to the Jacobson Radical
- Source :
- Mediterranean Journal of Mathematics. 14
- Publication Year :
- 2017
- Publisher :
- Springer Science and Business Media LLC, 2017.
-
Abstract
- Let R be a ring with identity and J(R) denote the Jacobson radical of R. A ring R is called J-reversible if for any a, $$b \in R$$ , $$ab = 0$$ implies $$ba \in J(R)$$ . In this paper, we give some properties of J-reversible rings. We prove that some results of reversible rings can be extended to J-reversible rings for this general setting. We show that J-quasipolar rings, local rings, semicommutative rings, central reversible rings and weakly reversible rings are J-reversible. As an application it is shown that every J-clean ring is directly finite.
- Subjects :
- Discrete mathematics
Reduced ring
Pure mathematics
Ring (mathematics)
Mathematics::Commutative Algebra
General Mathematics
010102 general mathematics
Local ring
010103 numerical & computational mathematics
Jacobson radical
01 natural sciences
Identity (mathematics)
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 16605454 and 16605446
- Volume :
- 14
- Database :
- OpenAIRE
- Journal :
- Mediterranean Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....87c01aaca4e0af5fa6b9624b6239f4cf