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Proceedings of the American Mathematical Society

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

 

 

Certain overrings of right hereditary, right Noetherian rings are $ V$-rings


Author: Friedhelm Hansen
Journal: Proc. Amer. Math. Soc. 52 (1975), 85-90
MSC: Primary 16A52
DOI: https://doi.org/10.1090/S0002-9939-1975-0376764-8
MathSciNet review: 0376764
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Abstract: It will be shown that a particular quotient ring of a ring $ R$ is a nontrivial $ V$-ring if $ R$ is a special kind of a right hereditary, right Noetherian ring. Another result states that all overrings of a right and left Goldie $ V$-ring, which is semiartinian modulo every essential right ideal, are $ V$-rings.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0376764-8
Keywords: $ V$-ring, hereditary and Noetherian ring, restricted minimum condition, quotient ring, overring
Article copyright: © Copyright 1975 American Mathematical Society