Abstract
The main result of this paper is a general approximation theorem for pairwise incomparable valuations on a commutative ring R in case that the intersection of the corresponding valuation rings is a R-Prüfer ring. As a corollary we obtain a general approximation theorem for rings with large Jacobson radical. We also get as a corollary a general approximation theorem for pairwise incomparable valuations on a total quotient ring T(A) of the Prüfer ring A, due to M. Arapović [2].
In the first part of this paper we deduce some results concerning R-Prüfer rings. We show that one form of the Chinese Remainder Theorem holds for a R-Prüfer ring A without Griffin’s extra assumption E⊂T(A)
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References
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© 1984 D. Reidel Publishing Company
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Alajbegović, J. (1984). R-Prüfer Rings and Approximation Theorems. In: van Oystaeyen, F. (eds) Methods in Ring Theory. NATO ASI Series, vol 129. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6369-6_1
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DOI: https://doi.org/10.1007/978-94-009-6369-6_1
Publisher Name: Springer, Dordrecht
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