J. Aust. Math. Soc.
76 (2004), 39-49
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On Noetherian rings with essential socle
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Jianlong Chen
Department of Mathematics
Nanjing University
Nanjing 210093
China
and
Department of Mathematics
Southeast University
Nanjing 210096
China
jlchen@seu.edu.cn
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Nanqing Ding
Department of Mathematics
Nanjing University
Nanjing 210093
China
nqding@nju.edu.cn
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Mohamed F. Yousif
Department of Mathematics
Ohio State University
Lima, Ohio 45804
USA
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 C F,
right F G F
and right Johns rings.
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