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http://dx.doi.org/10.4134/BKMS.b160541

A NOTE ON MINIMAL PRIME IDEALS  

Mohammadi, Rasul (Department of pure Mathematics Faculty of Mathematical Sciences Tarbiat Modares University)
Moussavi, Ahmad (Department of pure Mathematics Faculty of Mathematical Sciences Tarbiat Modares University)
Zahiri, Masoome (Department of Mathematics Faculty of Sciences Higher Education Center of Eghlid)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.4, 2017 , pp. 1281-1291 More about this Journal
Abstract
Let R be a strongly 2-primal ring and I a proper ideal of R. Then there are only finitely many prime ideals minimal over I if and only if for every prime ideal P minimal over I, the ideal $P/{\sqrt{I}}$ of $R/{\sqrt{I}}$ is finitely generated if and only if the ring $R/{\sqrt{I}}$ satisfies the ACC on right annihilators. This result extends "D. D. Anderson, A note on minimal prime ideals, Proc. Amer. Math. Soc. 122 (1994), no. 1, 13-14." to large classes of noncommutative rings. It is also shown that, a 2-primal ring R only has finitely many minimal prime ideals if each minimal prime ideal of R is finitely generated. Examples are provided to illustrate our results.
Keywords
minimal prime ideal; strongly 2-primal ring; duo ring;
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Times Cited By KSCI : 1  (Citation Analysis)
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