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Finiteness in prime ideals in rings of global dimension two


Author: Hu Sheng
Journal: Proc. Amer. Math. Soc. 41 (1973), 363-369
MSC: Primary 13C15
DOI: https://doi.org/10.1090/S0002-9939-1973-0327739-4
MathSciNet review: 0327739
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Abstract: Let $ A$ be a commutative ring with identity. The main result states conditions that ensure the finiteness of prime ideals in a coherent ring $ A$ of global dimension two. Precisely, any ideal containing two noncomparable prime ideals is finitely generated. As a corollary it follows that a Krull domain of global dimension two is noetherian. Another corollary is that if $ A$ is not semihereditary it contains a finitely generated maximal ideal.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0327739-4
Keywords: Coherent ring, Krull domain, global dimension, prime ideal
Article copyright: © Copyright 1973 American Mathematical Society

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