On the endomorphism ring of a module with relative chain conditions
作者:
Wu Quanshui,
Jonathan S. Golan,
期刊:
Communications in Algebra
(Taylor Available online 1990)
卷期:
Volume 18,
issue 8
页码: 2595-2609
ISSN:0092-7872
年代: 1990
DOI:10.1080/00927879008824041
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
A well-known result of Small states that if M is a noetherian left R-module having endomorphism ring S then any nil subring of S is nilpotent. Fisher [4] dualized this result and showed that if M is left artinian then any nil ideal of S is nilpotent. He gave a bound on the indices of nilpotency of nil subrings of the endomorphism rings of noetherian modules and raised the dual question of whether there are such bounds in the case of artinian modules. He gave an affirmative answer if the module is also assumed to be finitely-generated. Similar affirmative answers for modules with finite homogeneous length were given in [10] and [15]. On the other hand, the nilpotence of certain ideals of the endomorphism rings of modules noetherian relative to a torsion theory has been extensively studied. See [2,6,8,12,15,17]. Jirasko [11] dualized, in some sense, some of the results of [6] to torsion modules satisfying the descending chain conditions with respect to some radical.
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