A class of non-noetherian domains
Author:
James A. Huckaba
Journal:
Proc. Amer. Math. Soc. 24 (1970), 659-666
MSC:
Primary 13.15
DOI:
https://doi.org/10.1090/S0002-9939-1970-0254024-9
MathSciNet review:
0254024
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Abstract | References | Similar Articles | Additional Information
Abstract: A new class of non-noetherian domains, called $\beta$-domains, are characterized in the first part of this paper. The second part is concerned with deciding when the intersection of a $\beta$-domain with a valuation ring is again a $\beta$-domain.
- Shreeram Abhyankar, Ramification theoretic methods in algebraic geometry, Annals of Mathematics Studies, No. 43, Princeton University Press, Princeton, N.J., 1959. MR 0105416
- Maurice Auslander and David A. Buchsbaum, Homological dimension in local rings, Trans. Amer. Math. Soc. 85 (1957), 390–405. MR 86822, DOI https://doi.org/10.1090/S0002-9947-1957-0086822-7 N. Bourbaki, Algébre commutative, Chapitres 3, 5, 6, Actualités Sci. Indust., nos. 1293; 1308, Hermann, Paris, 1961; 1964. MR 30 #2027; MR 33 #2660.
- William Heinzer, Integral domains in which each non-zero ideal is divisorial, Mathematika 15 (1968), 164–170. MR 236161, DOI https://doi.org/10.1112/S0025579300002527 W. Heinzer and J. Ohm, Noetherian and non-noetherian commutative rings, Notices Amer. Math. Soc. 16 (1969), 264. Abstract #663-606.
- Noboru Nakano, Idealtheorie in einem speziellen unendlichen algebraischen Zahlkörper, J. Sci. Hiroshima Univ. Ser. A 16 (1953), 425–439 (German). MR 59316
- Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. MR 0120249
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Additional Information
Keywords:
Valuation ring,
nondiscrete valuations,
value group,
maximal ideal
Article copyright:
© Copyright 1970
American Mathematical Society