Research Article
Year 2021,
Volume: 42 Issue: 2, 321 - 326, 30.06.2021
Abstract
References
- [1] Kosan M. T., Lero A., Matczuk J. UJ rings, Commun. Algebra, 46 (5) (2018) 2297-2303.
- [2] Nicholson W.K., Lifting idempotent and exchange rings, Trans. Amer. Math. Soc., 229 (1977) 269-278.
- [3] Nicholso W.K., Zhou Y., Clean general rings, J. Algebra, 291 (2005) 297-311.
- [4] Lam T.Y., A First Course in Noncommutative Rings, GTM 131, 2nd ed. Verlag: Springer, (1991) 53-82.
- [5] Haghany A., Hopficity and co-hopficity for Morita contexts, Commun. Algebra, 27 (1999) 477-492.
- [6] Kosan M. T., The p.p. property of trivial extensions, J. Algebra Appl., 14 (8) (2015) 1550124.
- [7] Nicholson W.K., Zhou Y., Rings in which elements are uniquely the sum of an idempotent and a unit, Glasgow Math. J., 46 (2004) 227-236.
Year 2021,
Volume: 42 Issue: 2, 321 - 326, 30.06.2021
Abstract
The aim of this study is to characterize rings having the following properties for a non-trivial idempotent element e of R, U (eRe) = e + eJ(R)e = e + J (eRe) (and U (eRe) = e + N (eRe)),
where U (-), N (-) and J (-) denote the group of units, the set of all nilpotent elements and the Jacobson radical of R, respectively. In the present paper, some characterizations are also obtained in terms of every element is of the form e + u, where e2 = e ∈ R and u ∈ U(eRe).
References
- [1] Kosan M. T., Lero A., Matczuk J. UJ rings, Commun. Algebra, 46 (5) (2018) 2297-2303.
- [2] Nicholson W.K., Lifting idempotent and exchange rings, Trans. Amer. Math. Soc., 229 (1977) 269-278.
- [3] Nicholso W.K., Zhou Y., Clean general rings, J. Algebra, 291 (2005) 297-311.
- [4] Lam T.Y., A First Course in Noncommutative Rings, GTM 131, 2nd ed. Verlag: Springer, (1991) 53-82.
- [5] Haghany A., Hopficity and co-hopficity for Morita contexts, Commun. Algebra, 27 (1999) 477-492.
- [6] Kosan M. T., The p.p. property of trivial extensions, J. Algebra Appl., 14 (8) (2015) 1550124.
- [7] Nicholson W.K., Zhou Y., Rings in which elements are uniquely the sum of an idempotent and a unit, Glasgow Math. J., 46 (2004) 227-236.
There are 7 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | June 30, 2021 |
| Submission Date | June 3, 2020 |
| Acceptance Date | February 12, 2021 |
| Published in Issue | Year 2021Volume: 42 Issue: 2 |