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## SOME CHARACTERIZATIONS OF ARTINIAN RINGS

#### H. Khabazian [1]

##### 65 157

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.
prime, semiprime, semiprime-free, rAI-semiprime, Artinian, quasiBaer, QF, essential, annihilator
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• Department of Mathematical Sciences, Isfahan University of Technology Isfahan 84156-83111, Iran. e-mail: khabaz@cc.iut.ac.ir
Konular JA85BD23CD Makaleler Yazar: H. Khabazian
 Bibtex @ { ieja266310, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2011}, volume = {9}, pages = {1 - 9}, doi = {}, title = {SOME CHARACTERIZATIONS OF ARTINIAN RINGS}, key = {cite}, author = {Khabazian, H.} } APA Khabazian, H . (2011). SOME CHARACTERIZATIONS OF ARTINIAN RINGS. International Electronic Journal of Algebra, 9 (9), 1-9. Retrieved from http://dergipark.gov.tr/ieja/issue/25202/266310 MLA Khabazian, H . "SOME CHARACTERIZATIONS OF ARTINIAN RINGS". International Electronic Journal of Algebra 9 (2011): 1-9 Chicago Khabazian, H . "SOME CHARACTERIZATIONS OF ARTINIAN RINGS". International Electronic Journal of Algebra 9 (2011): 1-9 RIS TY - JOUR T1 - SOME CHARACTERIZATIONS OF ARTINIAN RINGS AU - H. Khabazian Y1 - 2011 PY - 2011 N1 - DO - T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 1 EP - 9 VL - 9 IS - 9 SN - 1306-6048-1306-6048 M3 - UR - Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra SOME CHARACTERIZATIONS OF ARTINIAN RINGS %A H. Khabazian %T SOME CHARACTERIZATIONS OF ARTINIAN RINGS %D 2011 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 9 %N 9 %R %U ISNAD Khabazian, H. . "SOME CHARACTERIZATIONS OF ARTINIAN RINGS". International Electronic Journal of Algebra 9 / 9 (Haziran 2011): 1-9.