Commutative Algebra -

Commutative Algebra

Noetherian and Non-Noetherian Perspectives
Buch | Softcover
492 Seiten
2014 | 2011 ed.
Springer-Verlag New York Inc.
978-1-4899-9004-4 (ISBN)
160,49 inkl. MwSt
Commutative Algebra presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. Topics include generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, and more.
Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra.


 


This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others.


 


This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.

- Introduction.- 1. Principal-like Ideals and Related Polynomial Content Conditions (D.D. Anderson).- 2. Zero-divisor Graphs in Commutative Rings (D.F. Anderson, M. Axtell, J. Stickles).- 3. Class Semigroups and T-class Semigroups of Domains (S. Bazzoni, S. Kabbaj).- 4. Forcing Algebras, Syzygy Bundles, and Tight Closure (H. Brenner).- 5. Beyond Totally Reflexive Modules and Back: A Survey on Gorenstein Dimensions (L.W. Christensen, H.B. Foxby, H. Holm).- 6. On V-domains: A Survey (M. Fontana, M. Zafrullah).- 7. Tensor Products of Algebras Over a Field (H. Haghighi, M. Tousi, S. Yassemi).- 8. Multiplicative Ideal Theory in the Context of Commutative Monoids (F. Halter-Koch).- 9. Projectively-Full Ideals and Compositions of Consistent Systems of Rank One Discrete Valuation Rings: A Survey (W. Heinzer, J. Ratliff, D. Rush).- 10. Direct-sum Behavior of Modules Over One-dimensional Rings (R. Karr, R. Wiegand).- 11. The Defect (F.V. Kuhlmann).- 12. The Use of Ultrafilters to Study the Structure of a Commutative Ring (K.A. Loper).- 13. Integrally Closed Overrings of Two-dimensional Noetherian Domains (B. Olberding).- 14. Almost Perfect Domains and Their Modules (L. Salce).- 15. Characteristic p Methods in Characteristic Zero via Ultraproducts (H. Schoutens).- 16. Rees Valuations (I. Swanson).- 17. Weak Normality and Seminormality (M. Vitulli).

Erscheint lt. Verlag 10.10.2014
Zusatzinfo VIII, 492 p.
Verlagsort New York
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 1-4899-9004-6 / 1489990046
ISBN-13 978-1-4899-9004-4 / 9781489990044
Zustand Neuware
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