An integrally closed ring which is not the intersection of valuation rings
HTML articles powered by AMS MathViewer
- by Joachim Gräter PDF
- Proc. Amer. Math. Soc. 107 (1989), 333-336 Request permission
Abstract:
Each commutative ring $R$ which is integrally closed in its total quotient ring $T(R)$ is the intersection of all paravaluation rings of $T(R)$ containing $R$. In this note an example is given that shows that this statement is not true with "valuation rings" instead of "paravaluation rings". This is an answer of a question asked by J. A. Huckaba in [3].References
- Nicolas Bourbaki, Elements of mathematics. Commutative algebra, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass., 1972. Translated from the French. MR 0360549
- J. Gräter, Integral closure and valuation rings with zero-divisors, Studia Sci. Math. Hungar. 17 (1982), no. 1-4, 457–458. MR 761562
- James A. Huckaba, Commutative rings with zero divisors, Monographs and Textbooks in Pure and Applied Mathematics, vol. 117, Marcel Dekker, Inc., New York, 1988. MR 938741
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 333-336
- MSC: Primary 13B20; Secondary 13A18
- DOI: https://doi.org/10.1090/S0002-9939-1989-0972231-9
- MathSciNet review: 972231