2011, XII, 488 p. 6 illus., 3 in color., Hardcover
ISBN: 978-1-4419-6989-7
Due: October 29, 2010
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.
- 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).
Series: Progress in Mathematics, Vol. 285
2010, XX, 230 p. 28 illus., Hardcover
ISBN: 978-0-8176-8091-6
Due: October 28, 2010
Explores Ramsey theory’s history, recent developments, and some promising future directions papers written by prominent researchers in the field
Provides historical background on the subject
Addresses Euclidean Ramsey theory and related coloring problems
Presents open problems throughout the volume
Ramsey theory is a relatively “new,” approximately 100 year-old direction of fascinating mathematical thought that touches on many classic fields of mathematics such as combinatorics, number theory, geometry, ergodic theory, topology, combinatorial geometry, set theory, and measure theory. Ramsey theory possesses its own unifying ideas, and some of its results are among the most beautiful theorems of mathematics. The underlying theme of Ramsey theory can be formulated as: any finite coloring of a large enough system contains a monochromatic subsystem of higher degree of organization than the system itself, or as T.S. Motzkin famously put it, absolute disorder is impossible. Ramsey Theory: Yesterday, Today, and Tomorrow explores the theory’s history, recent developments, and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys provide historical background on the subject; the last three address Euclidean Ramsey theory and related coloring problems. In addition, open problems posed throughout the volume and in the concluding open problem chapter will appeal to graduate students and mathematicians alike. Contributors: J. Burkert A. Dudek R.L. Graham A. Gyarfas P.D. Johnson, Jr. S.P. Radziszowski V. Rodl J.H. Spencer A. Soifer E. Tressler
How This Book Came into Being.- Table of Contents.- Ramsey Theory before Ramsey, Prehistory and Early History: An Essay in 13 Parts.- Eighty Years of Ramsey R(3, k). . . and Counting!.- Ramsey Numbers Involving Cycles.- On the function of Erd?s and Rogers.- Large Monochromatic Components in Edge Colorings of Graphs.- Szlam’s Lemma: Mutant Offspring of a Euclidean Ramsey Problem: From 1973, with Numerous Applications.- Open Problems in Euclidean Ramsey Theory.- Chromatic Number of the Plane and Its Relatives, History, Problems and Results: An Essay in 11 Parts.- Euclidean Distance Graphs on the Rational Points.- Open Problems Session.
Series: Lecture Notes in Mathematics, Vol. 2005
2011, X, 272 p., Softcover
ISBN: 978-3-642-14605-3
Due: October 2010
During the last 60 years the theory of function spaces has been a subject of growing interest and increasing diversity. Based on three formally different developments, namely, the theory of Besov and Triebel-Lizorkin spaces, the theory of Morrey and Campanato spaces and the theory of Q spaces, the authors develop a unified framework for all of these spaces. As a byproduct, the authors provide a completion of the theory of Triebel-Lizorkin spaces when p = ∞.
1 Introduction.- 2 The Spaces Bs,τp,q(Rn) and Fs,τp,q(Rn).- 3 Almost Diagonal Operators and Atomic and Molecular Decompositions.- 4 Several Equivalent Characterizations.- 5 Pseudo-differential Operators.- 6 Key Theorems.- 7 Inhomogeneous Besov-Hausdorff and Triebel-Lizorkin-Hausdorff Spaces.- 8 Homogeneous Spaces.
Series: Lecture Notes in Mathematics, Vol. 2007
2010, X, 166 p., Softcover
ISBN: 978-3-642-14827-9
Due: October 2010
This monograph deals with symmetries of compact Riemann surfaces. A symmetry of a compact Riemann surface S is an antianalytic involution of S. It is well known that Riemann surfaces exhibiting symmetry correspond to algebraic curves which can be defined over the field of real numbers. In this monograph we consider three topics related to the topology of symmetries, namely the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.
1 Preliminaries.- 2 Number of Conjugacy Classes of Symmetries.- 3 Counting Ovals of Symmetries.- 4 Symmetry Types of some Families of Riemann Surfaces.- 5 Symmetry Types of Riemann Surfaces with a Large Group of Automorphisms.- 6 Appendix
2011, 290 p. 35 illus., Hardcover
ISBN: 978-1-4419-7328-3
Due: December 13, 2010
Unlike most books on homotopy theory, the unifying theme of this textbook is the Eckmann-Hilton duality theory, not to be found elsewhere in available literature. With a wealth of illustrations and exercises, this book motivates the reader in a way which is is often missing in most books on the subject. This carefully written text moves at a gentle pace, even with fairly advanced material. Each exercise indicates the level of difficulty, and there are also hints to some of the harder exercises at the end of the book.
*H-Spaces and Co-H-Spaces;
*cofibrations and fibrations;
*exact sequences;
*applications of exactness;
*homotopy pushouts and pullbacks;
*homotopy and homology decompositions;
*homotopy sets; and
*obstruction theory.
1 Basic Homotopy.- 1.1 Introduction.- 1.2 Spaces, Maps, Products and Wedges.- 1.3 Homotopy I.- 1.4 Homotopy II.- 1.5 CW Complexes.- 1.6 Why Study Homotopy Theory?.- 1.7 Exercises.- 2 H-Spaces and Co-H-Spaces.- 2.1 H-Spaces and Co-H-Spaces.- 2.2 Loop Spaces and Suspensions.- 2.3 Homotopy Groups I.- 2.4 Moore Spaces and Eilenberg-Mac Lane Spaces.- 2.5 Eckmann-Hilton Duality I.- 2.6 Exercises.- 3 Cofibrations and Fibrations.- 3.1 Introduction.- 3.2 Cofibrations.- 3.3 Fibrations.- 3.4 Examples of Fiber Bundles.- 3.5 Replacing a Map by a Cofiber or Fiber Map.- 3.6 Exercises.- 4 Exact Sequences.- 4.1 The Coexact and Exact Sequence of a Map.- 4.2 Actions and Coactions.- 4.3 Operations.- 4.4 Homotopy Groups II.- 4.5 Exercises.- 5 Applications of Exactness.- 5.1 Universal Coefficient Theorems.- 5.2 Homotopical Cohomology Groups.- 5.3 Applications to Fiber and Cofiber Sequences.- 5.4 The Operation of the Fundamental Group.- 5.5 Calculation of Homotopy Groups.- 5.6 Exercises.- 6 Homotopy Pushouts and Pullbacks.- 6.1 Homotopy Pushouts and Pullbacks I.- 6.2 Homotopy Pushouts and Pullbacks II.- 6.3 Theorems of Serre, Hurewicz and Blakers-Massey.- 6.4 Eckmann-Hilton Duality II.- 6.5 Exercises.- 7 Homotopy and Homology Decompositions.- 7.1 Introduction.- 7.2 Homotopy Decompositions of Spaces.- 7.3 Homology Decompositions of Spaces.- 7.4 Homotopy and Homology Decompositions of Maps.- 7.5 Exercises.- 8 Homotopy Sets.- 8.1 The Set [X, Y ].- 8.2 Category.- 8.3 Loop and Group Structure in [X, Y ].- 8.4 Exercises.- 9 Obstruction Theory.- 9.1 Introduction.- 9.2 Obstructions Using Homotopy Decompositions.- 9.3 Lifts and Extensions.- 9.4 Obstruction Miscellany.- 9.5 Exercises.- 10 Appendices (Outlined).- 10.1 Appendix A: Point-Set Topology.- 10.2 Appendix B: The Fundamental Group.- 10.3 Appendix C: Homology and Cohomology.- 10.4 Appendix D: The nth and (n+1)st Homotopy Group of the n-Sphere.- 10.5 Appendix E: Homotopy Pushouts and Pullbacks.- 10.6 Appendix F: Categories and Functors.- Hints to Some of the Exercises.- Bibliography.- Index.- PICTURES