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 be a finitely generated module over a subring of its center. Then it will be shown that has the property that every right ideal can be generated by a bounded number of elements if and only if 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

Article copyright:
© Copyright 1986
American Mathematical Society