The Resource Manis valuations and Prüfer extensions I : a new chapter in commutative algebra, Manfred Knebusch, Digen Zhang

Manis valuations and Prüfer extensions I : a new chapter in commutative algebra, Manfred Knebusch, Digen Zhang

Label
Manis valuations and Prüfer extensions I : a new chapter in commutative algebra
Title
Manis valuations and Prüfer extensions I
Title remainder
a new chapter in commutative algebra
Statement of responsibility
Manfred Knebusch, Digen Zhang
Title variation
Shan shu bu yong chou ce
Creator
Contributor
Subject
Language
eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorName
Knebusch, Manfred
Illustrations
illustrations
Index
index present
LC call number
QA3
LC item number
.L28 no. 1791
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1965-
http://library.link/vocab/relatedWorkOrContributorName
Zhang, Digen
Series statement
Lecture notes in mathematics,
Series volume
1791
http://library.link/vocab/subjectName
  • Prüfer rings
  • Graph labelings
  • Commutative algebra
  • Prüfer, Anneaux de
  • Étiquetage de graphes
  • Algèbre commutative
  • Commutative algebra
  • Graph labelings
  • Prüfer rings
Label
Manis valuations and Prüfer extensions I : a new chapter in commutative algebra, Manfred Knebusch, Digen Zhang
Instantiates
Publication
Note
Continued by: Manis valuations and Prüfer extensions II (Lecture notes in mathematics (Springer Verlag) ; 2103)
Bibliography note
Includes bibliographical references (p. [257]-262) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
Dimensions
24 cm.
Extent
267 pages
Isbn
9783540439516
Lccn
2002029197
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
System control number
  • (OCoLC)50253198
  • (OCoLC)ocm50253198
Label
Manis valuations and Prüfer extensions I : a new chapter in commutative algebra, Manfred Knebusch, Digen Zhang
Publication
Note
Continued by: Manis valuations and Prüfer extensions II (Lecture notes in mathematics (Springer Verlag) ; 2103)
Bibliography note
Includes bibliographical references (p. [257]-262) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
Dimensions
24 cm.
Extent
267 pages
Isbn
9783540439516
Lccn
2002029197
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
System control number
  • (OCoLC)50253198
  • (OCoLC)ocm50253198

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