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Manis valuations and Prüfer extensions I : a new chapter in commutative algebra

Author: Manfred Knebusch; Digen Zhang
Publisher: Berlin ; New York : Springer, ©2002.
Series: Lecture notes in mathematics (Springer-Verlag), 1791.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:

For further develomemt of real algebraic and real analytic geometry, new chapters of commutative algebra are needed, often of a non-noetherian nature. This volume is devoted to a study of relative  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Manfred Knebusch; Digen Zhang
ISBN: 354043951X 9783540439516
OCLC Number: 50253198
Notes: Continued by: Manis valuations and Prüfer extensions II (Lecture notes in mathematics (Springer Verlag) ; 2103)
Description: 267 p. ; 24 cm.
Contents: 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.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1791.
Other Titles: Shan shu bu yong chou ce
Responsibility: Manfred Knebusch, Digen Zhang.
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