Year 2011, Volume 9, Issue 9, Pages 1 - 9 2011-06-01

SOME CHARACTERIZATIONS OF ARTINIAN RINGS

H. Khabazian [1]

74 201

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
  • 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
Other ID JA85BD23CD
Journal Section Articles
Authors

Author: H. Khabazian

Dates

Publication Date: June 1, 2011

Bibtex @ { ieja266310, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {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.org.tr/ieja/issue/25202/266310
MLA Khabazian, H . "SOME CHARACTERIZATIONS OF ARTINIAN RINGS". International Electronic Journal of Algebra 9 (2011): 1-9 <http://dergipark.org.tr/ieja/issue/25202/266310>
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 (June 2011): 1-9.
AMA Khabazian H . SOME CHARACTERIZATIONS OF ARTINIAN RINGS. IEJA. 2011; 9(9): 1-9.
Vancouver Khabazian H . SOME CHARACTERIZATIONS OF ARTINIAN RINGS. International Electronic Journal of Algebra. 2011; 9(9): 9-1.