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Proceedings of the American Mathematical Society

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

 

 

Unibranched prime ideals and going down in PI rings


Author: Phillip Lestmann
Journal: Proc. Amer. Math. Soc. 82 (1981), 191-195
MSC: Primary 16A33; Secondary 16A38
DOI: https://doi.org/10.1090/S0002-9939-1981-0609649-2
MathSciNet review: 609649
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Abstract: The purpose of this paper is to answer the question of whether going down is equivalent to unibranchedness of prime ideals in integral extensions of prime $ {\text{PI}}$ rings. We show by example that, in general, the answer is no; and we find an additional condition which, together with going down, implies prime ideals of $ {\text{ht}} > 1$ are unibranched.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0609649-2
Keywords: Integral extension, integral closure, going down, prime ideal, $ {\text{PI}}$ ring, Noetherian, unibranched
Article copyright: © Copyright 1981 American Mathematical Society