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Proceedings of the American Mathematical Society

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

 

 

Minimal primes of ideals and integral ring extensions


Author: William Heinzer
Journal: Proc. Amer. Math. Soc. 40 (1973), 370-372
MSC: Primary 13A15
DOI: https://doi.org/10.1090/S0002-9939-1973-0319962-X
MathSciNet review: 0319962
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Abstract: It is shown that if $ R$ is a commutative ring with identity having the property that ideals in $ R$ have only a finite number of minimal primes, then a finite $ R$-algebra again has this property. It is also shown that an almost finite integral extension of a noetherian integral domain has noetherian prime spectrum.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0319962-X
Keywords: Minimal primes of an ideal, integral ring extension, noetherian integral domain, derived normal ring, noetherian prime spectrum
Article copyright: © Copyright 1973 American Mathematical Society