Finiteness in prime ideals in rings of global dimension two
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- by Hu Sheng
- Proc. Amer. Math. Soc. 41 (1973), 363-369
- DOI: https://doi.org/10.1090/S0002-9939-1973-0327739-4
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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.References
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- 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