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Proceedings of the American Mathematical Society

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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.


References [Enhancements On Off] (What's this?)

  • [1] W. Heinzer, A note on rings with noetherian spectrum, Duke Math. J. 38 (1970), 573-578. MR 41 #8395. MR 0263795 (41:8395)
  • [2] M. Nagata, Local rings, Interscience Tracts in Pure and Appl. Math., no. 13, Interscience, New York, 1962. MR 27 #5790. MR 0155856 (27:5790)
  • [3] J. Ohm and R. Pendleton, Rings with noetherian spectrum, Duke Math. J. 35 (1968), 631-639. MR 37 #5201. MR 0229627 (37:5201)

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Additional Information

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

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