Locally affine ring extensions of a Noetherian domain
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- by William Heinzer PDF
- Proc. Amer. Math. Soc. 35 (1972), 377-380 Request permission
Abstract:
If $A \subset R$ are integral domains with A noetherian, it is shown that if R is contained in an affine ring over A and if for each maximal ideal P of A with $S = A\backslash P,{R_S}$ is an affine ring over ${A_P}$, then R itself is affine over A.References
- Paul Eakin and James Silver, Rings which are almost polynomial rings, Trans. Amer. Math. Soc. 174 (1972), 425–449. MR 309924, DOI 10.1090/S0002-9947-1972-0309924-4
- Robert W. Gilmer, Multiplicative ideal theory, Queen’s Papers in Pure and Applied Mathematics, No. 12, Queen’s University, Kingston, Ont., 1968. MR 0229624
- Irving Kaplansky, Commutative rings, Allyn and Bacon, Inc., Boston, Mass., 1970. MR 0254021
- Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155856
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 377-380
- MSC: Primary 13B99
- DOI: https://doi.org/10.1090/S0002-9939-1972-0304364-1
- MathSciNet review: 0304364