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On *-modules over valuation rings. (English) Zbl 0716.13017

Unter einem Bewertungsring versteht der Verf. einen kommutativen Ring - nicht notwendig nullteilerfrei - mit linear geordnetem Idealverband. Das Hauptergebnis ist der Satz, daß ein endlich erzeugter *-Modul über einem Bewertungsring R zu \((R/A)^ n\), \(n\geq 0\), A Ideal von R, isomorph ist. *-Moduln sind hierbei kategorien-theoretisch durch eine gewisse Dualitätsforderung definiert.
Reviewer: K.Mathiak

MSC:

13F30 Valuation rings
13A18 Valuations and their generalizations for commutative rings
13A05 Divisibility and factorizations in commutative rings
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References:

[1] R. Colpi , Some remarks on equivalence between categories of modules , to appear on Comm. in Algebra . MR 1071082 | Zbl 0708.16002 · Zbl 0708.16002 · doi:10.1080/00927879008824002
[2] R. Colpi - C. Menini , On the structure of *-modules , to appear. MR 1226797 | Zbl 0795.16005 · Zbl 0795.16005 · doi:10.1006/jabr.1993.1138
[3] G. D’Este , Some remarks on representable equivalences , to appear in the Proceedings of the Banach Center . Zbl 0722.16007 · Zbl 0722.16007
[4] G. D’Este - D. Happel , Representable equivalences are represented by tilting modules , to appear on Rend. Sem. Mat. Univ. Padova . Numdam | MR 1066430 | Zbl 0706.16011 · Zbl 0706.16011
[5] L. Fuchs - L. Salce , Modules over valuation domains , Lecture Notes in Pure Appl. Math. , n. 97 , Marcel Dekker , New York , 1985 . MR 786121 | Zbl 0578.13004 · Zbl 0578.13004
[6] L. Fuchs - L. SALCE, Equivalent categories of divisible modules , Forum Math. , 1 ( 1989 ). Article | MR 1030623 | Zbl 0691.13001 · Zbl 0691.13001 · doi:10.1515/form.1990.2.1
[7] E. Matlis , Cotorsion modules , Mem. Amer. Math. Soc. , 49 ( 1964 ). MR 178025 | Zbl 0135.07801 · Zbl 0135.07801
[8] C. Menini - A. Orsatti , Representable equivalences between categories of modules and applications , to appear on Rend. Sem. Mat. Univ. Padova . Numdam | MR 1049594 | Zbl 0701.16007 · Zbl 0701.16007
[9] L. Salce - P. ZANARDO, Finitely generated modules over valuation rings , Comm. Algebra , 12 ( 15 ), ( 1984 ), pp. 1795 - 1812 . MR 745167 | Zbl 0539.13007 · Zbl 0539.13007 · doi:10.1080/00927878408823083
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