Actions for Manis valuations and Prüfer extensions I [electronic resource] : a new chapter in commutative algebra

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Manis valuations and Prüfer extensions I [electronic resource] : a new chapter in commutative algebra / Manfred Knebusch, Digen Zhang

Author
Knebusch, Manfred
Additional Titles
Cover title also in Chinese: Shan shu bu yong chou ce
Published
Berlin ; New York : Springer, [2002]
Copyright Date
©2002
Physical Description
267 pages ; 24 cm.
Additional Creators
Zhang, Digen, 1965-
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Contents
Machine generated contents note: Ch. I Basics on Manis valuations and Prufer extensions -- 1.Valuations of rings -- 2.Valuation subrings and Manis pairs -- 3.Weakly surjective homomorphisms -- 4.More on weakly surjective extensions -- 5.Basic theory of Prufer extensions -- 6.Examples of Prufer extensions and convenient ring extensions -- 7.Principal ideal results -- Ch. II Multiplicative ideal theory -- 1.Multiplicative properties of regular modules -- 2.Characterizing Prufer extensions' by the behavior of their regular ideals -- 3.Describing a Prufer extension by its lattice of regular ideals -- 4.Tight extensions -- 5.Distributive submodules -- 6.Transfer theorems -- 7.Polars and factors in a Prufer extension -- 8.Decomposition of regular modules -- 9.Prufer overmodules -- 10.Bezout extensions -- 11.The Prufer extensions of a noetherian ring -- 12.Invertible hulls for modules over noetherian rings -- Ch. III PM-valuations and valuations of weaker type -- 1.The PM-overrings in a Prufer extension -- 2.Regular modules in a PM-extension -- 3.More ways to characterize PM-extensions, and a look at BM-extensions -- 4.Tight valuations -- 5.Existence of various valuation hulls -- 6.Inside and outside the Manis valuation hull -- 7.The TV-hull in a valuative extension -- 8.Principal valuations -- 9.Descriptions of the PM-hull -- 10.Composing valuations with ring homomorphisms -- 11.Transfer of valuations -- App. A (to I, Session 4 and I, Session 5): Flat epimorphisms -- App. B (to II, Session 2): Arithmetical rings -- App. C (to III, Session 6): A direct proof of the existence of Manis valuation hulls.
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ISBN
354043951X (softcover : acid-free paper)
Bibliography Note
Includes bibliographical references (pages [257]-262) and indexes.
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