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Commutative Algebra : Noetherian and Non-Noetherian Perspectives / edited by Marco Fontana, Salah-Eddine Kabbaj, Bruce Olberding, Irena Swanson

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: New York, NY : Springer New York, 2011Description: Online-Ressource (VIII, 492p. 3 illus, digital)ISBN:
  • 9781441969903
Subject(s): Genre/Form: Additional physical formats: 9781441969897 | Buchausg. u.d.T.: Commutative algebra. New York, NY[u.a.] : Springer Science+Business Media, LLC, 2011. VIII, 492 S.DDC classification:
  • 512.44
MSC: MSC: *13-06 | 00B15 | 13Axx | 13Cxx | 13ExxLOC classification:
  • QA251.3
DOI: DOI: 10.1007/978-1-4419-6990-3Online resources: Summary: - 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).Summary: 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 are internationally renowned for their important contributions to various aspects of current research in commutative algebra. 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 commutative algebra.PPN: PPN: 1650423527Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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