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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rings with a bounded number of generators for right ideals


Author: William D. Blair
Journal: Proc. Amer. Math. Soc. 98 (1986), 1-6
MSC: Primary 16A33; Secondary 13E05, 16A38
MathSciNet review: 848862
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Abstract: Let the ring $ S$ be a finitely generated module over a subring $ R$ of its center. Then it will be shown that $ S$ has the property that every right ideal can be generated by a bounded number of elements if and only if $ R$ has the property that every ideal can be generated by a bounded number of elements. As a corollary we show that a two-sided Noetherian affine ring satisfying a polynomial identity has the property that every right ideal can be generated by a bounded number of elements if and only if every left ideal can be generated by a bounded number of elements.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0848862-0
PII: S 0002-9939(1986)0848862-0
Article copyright: © Copyright 1986 American Mathematical Society