Abstract
References
- Chiba, K. and Tominaga, H. On strongly regular rings, Proc. Japan Acad. 49, 435–437, 1973.
- Divinsky, N. J. Rings and radicals (University of Toronto Press, 1965).
- Kaya, A. One sided ideals of a strongly prime type (Proc. I. National Mathematics Sympo- sium, Ankara, 31 Aug.-2 Sept, 1988), 95–96.
- Kaya, A. and Kuzucuoglu, F. On strongly regular rings, Turkish J. Math. 20, 395–398, 1996.
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- Koh, K. On one sided ideals of a prime type, Proc. Amer. Math. Soc. 28, 321–329, 1971.
- Koh, K. Quasisimple modules and other topics in ring theory. Lectures on rings and modules (Lecture Notes in Math. 246, Springer-Verlag, Berlin, 1972).
- Mogami, I. and Hongan, M. Note on commutativity of rings, Math. J. Okayama Univ. 20, 21–24, 1978.
- Rosenberg, A. L. The left spectrum, the Levitzki radicals, noncommutative schemes, Proc. Natl. Acad. Sci. USA 87, 8583–8586, 1990.
- Tominaga, H. On s-unital rings, Math. J. Okayama Univ. 18, 117–133, 1976.
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Abstract
The notion of strongly prime right ideal is analogous to that of completely prime ideal in a commutative ring. We prove that the intersection of all strongly prime right ideals of a ring R coincides with the Levitzki radical of this ring. We also give various conditions on a noncommutative ring R so that R is 2-primal.
Keywords
Prime right ideal Strongly prime right ideal 2-primal ring AC-ring Regular ring 2000 AMS Classification: 17 B 40
References
- Chiba, K. and Tominaga, H. On strongly regular rings, Proc. Japan Acad. 49, 435–437, 1973.
- Divinsky, N. J. Rings and radicals (University of Toronto Press, 1965).
- Kaya, A. One sided ideals of a strongly prime type (Proc. I. National Mathematics Sympo- sium, Ankara, 31 Aug.-2 Sept, 1988), 95–96.
- Kaya, A. and Kuzucuoglu, F. On strongly regular rings, Turkish J. Math. 20, 395–398, 1996.
- Kim, N. K. and Lee, Y. On right quasi-duo rings which are π-regular, Bull. Korean Math. Soc. 37, 217–227, 2000.
- Koh, K. On one sided ideals of a prime type, Proc. Amer. Math. Soc. 28, 321–329, 1971.
- Koh, K. Quasisimple modules and other topics in ring theory. Lectures on rings and modules (Lecture Notes in Math. 246, Springer-Verlag, Berlin, 1972).
- Mogami, I. and Hongan, M. Note on commutativity of rings, Math. J. Okayama Univ. 20, 21–24, 1978.
- Rosenberg, A. L. The left spectrum, the Levitzki radicals, noncommutative schemes, Proc. Natl. Acad. Sci. USA 87, 8583–8586, 1990.
- Tominaga, H. On s-unital rings, Math. J. Okayama Univ. 18, 117–133, 1976.
- Tominaga, H. On s-unital rings II, Math. J. Okayama Univ. 19, 171–182, 1977.
- Wong, E. T. Almost commutative rings and their integral extensions, Math. J. Okayama
- Univ. 18 (2), 105–111, 1976.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | April 1, 2010 |
| Published in Issue | Year 2010 Volume: 39 Issue: 4 |