Öz
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.
Anahtar Kelimeler
prime semiprime semiprime-free rAI-semiprime Artinian quasiBaer QF essential annihilator
Kaynakça
- 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
Öz
Kaynakça
- 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
Ayrıntılar
| Diğer ID | JA85BD23CD |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Haziran 2011 |
| Yayımlandığı Sayı | Yıl 2011 Cilt: 9 Sayı: 9 |