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SOME CHARACTERIZATIONS OF ARTINIAN RINGS

Year 2011, Volume: 9 Issue: 9 , 1 - 9 , 01.06.2011

H. Khabazian

https://izlik.org/JA57EH22WC

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.

Keywords

prime semiprime semiprime-free rAI-semiprime Artinian quasiBaer QF essential annihilator

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

H. Khabazian

https://izlik.org/JA57EH22WC

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
Authors

H. Khabazian This is me

Publication Date June 1, 2011
IZ https://izlik.org/JA57EH22WC
Published in Issue Year 2011 Volume: 9 Issue: 9

Cite

APA Khabazian, H. (2011). SOME CHARACTERIZATIONS OF ARTINIAN RINGS. International Electronic Journal of Algebra, 9(9), 1-9. https://izlik.org/JA57EH22WC
AMA 1.Khabazian H. SOME CHARACTERIZATIONS OF ARTINIAN RINGS. IEJA. 2011;9(9):1-9. https://izlik.org/JA57EH22WC
Chicago Khabazian, H. 2011. “SOME CHARACTERIZATIONS OF ARTINIAN RINGS”. International Electronic Journal of Algebra 9 (9): 1-9. https://izlik.org/JA57EH22WC.
EndNote Khabazian H (June 1, 2011) SOME CHARACTERIZATIONS OF ARTINIAN RINGS. International Electronic Journal of Algebra 9 9 1–9.
IEEE [1]H. Khabazian, “SOME CHARACTERIZATIONS OF ARTINIAN RINGS”, IEJA, vol. 9, no. 9, pp. 1–9, June 2011, [Online]. Available: https://izlik.org/JA57EH22WC
ISNAD Khabazian, H. “SOME CHARACTERIZATIONS OF ARTINIAN RINGS”. International Electronic Journal of Algebra 9/9 (June 1, 2011): 1-9. https://izlik.org/JA57EH22WC.
JAMA 1.Khabazian H. SOME CHARACTERIZATIONS OF ARTINIAN RINGS. IEJA. 2011;9:1–9.
MLA Khabazian, H. “SOME CHARACTERIZATIONS OF ARTINIAN RINGS”. International Electronic Journal of Algebra, vol. 9, no. 9, June 2011, pp. 1-9, https://izlik.org/JA57EH22WC.
Vancouver 1.H. Khabazian. SOME CHARACTERIZATIONS OF ARTINIAN RINGS. IEJA [Internet]. 2011 Jun. 1;9(9):1-9. Available from: https://izlik.org/JA57EH22WC