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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A right PCI ring is right Noetherian


Author: Robert F. Damiano
Journal: Proc. Amer. Math. Soc. 77 (1979), 11-14
MSC: Primary 16A46
MathSciNet review: 539620
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Abstract: C. Faith and J. Cozzens have shown that a ring, whose right proper cyclic modules are injective, is either semisimple or a simple, right semihereditary, right Ore V-domain. They have posed a question as to whether such a ring is right noetherian. In this paper, an affirmative answer is given to that question. Moreover, necessary and sufficient conditions are given as to when a right PCI ring is left PCI.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0539620-1
Article copyright: © Copyright 1979 American Mathematical Society