1st Edition

Rings, Modules, Algebras, and Abelian Groups

Edited By Alberto Facchini, Evan Houston, Luigi Salce Copyright 2004
    526 Pages
    by CRC Press

    526 Pages
    by CRC Press

    Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological algebraic structures, and provides more than 600 current references and 570 display equations for further exploration of the topic. It provides stimulating discussions from world-renowned names including Laszlo Fuchs, Robert Gilmer, Saharon Shelah, Daniel Simson, and Richard Swan to celebrate 40 years of study on cumulative rings.

    Describing emerging theories

    Preface, Participants to the Conference, Contributors, 1. Additives Galois Theory of Modules, 2. Finitely Generated and Cogenerated QD Groups, 3. Direct Limits of Modules of Finite Projective Dimension. 4. Classification of a Class of Almost Completely Decomposable Groups, 5. A Polynomial Ring Sampler, 6. The Picard Group of the Ring of Integer-valued Polynomials on a Valuation Domain, 7. A Note on Cotilting Modules and Generalized Morita Duality, 8. Dualities Induced by Cotilting Bimodules, 9. Symmetries and Asymmetries for Cotilting Bimodules, 10. A Constructive Solution to the Base Change Decomposition Problem in B(1)-groups, 11. On a Property of the Adele Ring of the Rationals, 12. On Strong Going-between, Going-down, and their Universalizations, 13. Factorization of Divisorial Ideals in a Generalized Krull Domain, 14. Divisorial Multiplication Rings, 15. Global Deformations of Lie Algebras, 16. Maximal Prime Divisors in Arithmetical Rings, 17. On Strongly Flat Modules over Matlis Domains, 18. Group Identities on Unit Groups of Group Algebras, 19. Forty Years of Commutative Ring Theory, 20. Modules Induced from a Normal Subgroup of Prime Index, 21. Uniquely Transitive Torsion-free Abelian Groups, 22. Generalized .E-rings, 23. Butler Modules and Bext, 24. Remarks on the Multiplicative Structure of Certain One-dimensional Integral Domains, 25. Non-fmitely Generated Prime Ideals in Subrings of Power Series Rings, 26. Rings with Finitely Many Orbits under the Regular Action, 27. Projective Covers and Injective Hulls in Abelian Length Categories, 28. Semigroup Rings that Are Inside Factorial and Their Cale Representation, 29. Reduced Modules, 30. The Mori Property in Rings with Zero Divisors, 31. Minimal Prime Ideals and Generalizations of Factorial Domains, 32. Factorizations of Monic Polynomials, 33. Monotone Complete Ordered Fields, Generalized Power Series, and Integer Parts, 34. On Distance between Finite Rings, 35. Affine Pairs, 36. When a Super-decomposable Pure-injective Module over a Serial Ring Exists, 37. Path Coalgebras of Quivers with Relations and a Tame-wild Dichotomy Problem for Coalgebras, 38. On Central Galois Algebras of a Galois Algebra


    Alberto Facchini is Professor of Mathematics, University of Padua, Italy. The author or coauthor of numerous professional publications, he is a member of the European Mathematical Society, the American Mathematical Society, and the Scientific Advisory Board of the Centre de Recerca Matematica, Barcelona. Professor Facchini serves on the editorial board of Communications in Algebra (Marcel Dekker, Inc.), among other journals. He received the doctoral degree in mathematics (1977) from the University of Padua, Italy. Evan Houston is Professor of Mathematics, University of North Carolina at Charlotte. The author or coeditor of numerous professional publications including Commutative Ring Theory (Marcel Dekker, Inc.), his research focuses on commutative algebra. He received the PH.D. degree (1973) from the University of Texas at Austin. Luigi Salce is Professor of Linear Algebra, University of Padua, Italy. He is the author, coauthor, editor or coeditor of many papers and books on abelian groups and module theory, including Modules Over Valuation Domains and Abelian Groups, Module Theory, and Topology (both titles, Marcel Dekker, Inc.). A member of the Italian Mathematical Union, Dr. Salce received the doctoral degree (1969) in mathematics from the University of Padua, Italy.

    "This book collects stimulating discussions from world-renowned names … . [It] celebrates the past 40 years of study on commutative rings … and presents new perspectives on connections between ring theoretic and module theoretic results. "
    - L'Enseignement Mathematique, Vol. 50, 1-2, Jan-Jun 2004

    "The book is indispensable for anyone interested in current trends and methods of ring and model theory."
    -EMS Newsletter, June 2005