Year 2011,
Volume: 9 Issue: 9, 1 - 9, 01.06.2011
Abstract
In this paper, we investigate rings in which the prime radical is an annihilator and present a characterization of Artinian rings satisfying this property. We also study rings in which the singular ideal and the prime radical coincide. Finally we show that Artinian rings are the direct product of a semiprime ring and a semiprime-free ring (ring in which every nonzero ideal contains a nonzero nilpotent ideal) and present a result on quasi-Baer Artinian rings.
References
- W. E. Clark, Twisted matrix units semigroup algebra, Duke Math. J., 34 (1967), 423.
- P. M. Cohn, Reversible rings, Bull. London Math. Soc., 31 (1999), 641-648.
- H. Khabazian, Primary decomposition for noncommutative rings, Vietnam J. Math., 36(2) (2008), 183-190.
- T.Y. Lam, Lectures on Modules and Rings, Springer-Verlag, 1998.
- D. S. Passman, Infinite Group Ring, Marcel Dekker Inc, 1971. H. Khabazian
- Department of Mathematical Sciences, Isfahan University of Technology Isfahan 84156-83111, Iran. e-mail: khabaz@cc.iut.ac.ir
Year 2011,
Volume: 9 Issue: 9, 1 - 9, 01.06.2011
Abstract
References
- W. E. Clark, Twisted matrix units semigroup algebra, Duke Math. J., 34 (1967), 423.
- P. M. Cohn, Reversible rings, Bull. London Math. Soc., 31 (1999), 641-648.
- H. Khabazian, Primary decomposition for noncommutative rings, Vietnam J. Math., 36(2) (2008), 183-190.
- T.Y. Lam, Lectures on Modules and Rings, Springer-Verlag, 1998.
- D. S. Passman, Infinite Group Ring, Marcel Dekker Inc, 1971. H. Khabazian
- Department of Mathematical Sciences, Isfahan University of Technology Isfahan 84156-83111, Iran. e-mail: khabaz@cc.iut.ac.ir
There are 6 citations in total.
Details
| Other ID | JA85BD23CD |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | June 1, 2011 |
| Published in Issue | Year 2011 Volume: 9 Issue: 9 |