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On Noetherian rings with essential socle

Published online by Cambridge University Press:  09 April 2009

Jianlong Chen ,
Nanqing Ding  and
Mohamed F. Yousif
Jianlong Chen
Affiliation:
Department of Mathematics, Nanjing UniversityNanjing 210093, China and Department of Mathematices, Southeast University, Nanjing 210096, China, e-mail: jlchen@seu.edu.cn
Nanqing Ding
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, China, e-mail: nqding@nju.edu.cn
Mohamed F. Yousif
Affiliation:
Department of Mathematics, Ohio State University, Lima, Ohio 45804, USA, e-mail: yousif.1@osu.edu
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Abstract

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It is shown that if R is a right Noetherian ring whose right socle is essential as a right ideal and is contained in the left socle, then R is right Artinian. This result may be viewed as a one-sided version of a result of Ginn and Moss on two-sided Noetherian rings with essential socle. This also extends the work of Nicholson and Yousif where the same result is obtained under a stronger hypothesis. We use our work to obtain partial positive answers to some open questions on right CF, right FGF and right Johns rings.

Keywords

Noetherian ringsArtinian ringsquasi-Frobenius rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 1 , February 2004 , pp. 39 - 50
Copyright
Copyright © Australian Mathematical Society 2004

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