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Proceedings of the American Mathematical Society

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

 

 

The $ n$-generator property for commutative rings


Author: Robert Gilmer
Journal: Proc. Amer. Math. Soc. 38 (1973), 477-482
DOI: https://doi.org/10.1090/S0002-9939-1973-0309922-7
MathSciNet review: 0309922
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Abstract | References | Additional Information

Abstract: Let $ D$ be an integral domian with identity. If for some positive integer $ n$, each finitely generated ideal of $ D$ has a basis of $ n$ elements, then the integral closure of $ D$ is a Prüfer domain. This result generalizes to the case of commutative rings with identity that contain zero divisors.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0309922-7
Keywords: Generating sets for ideals, Prüfer rings, finite rank
Article copyright: © Copyright 1973 American Mathematical Society