Rings, modules, algebras and abelian groups : proceedings of the algebra conference--Venezia

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 The Algebra Conference - Venezia 2002 was held at the Venice International University (VTU) on the beautiful island of San Servolo in the Venice lagoon, from June 3 to 8, 2002. More than 190 mathematicians from 35 different countries attended the conference. The participants made the conference quite stimulating. It was organized in 12 main lectures and 6 plenary lectures in the mornings, and in six different sections in the afternoons, where more than 110 communications were presented. The six sections were as follows: Abelian groups, algebras and their representations, commutative rings, module theory, ring theory, and topological algebraic structures. The content of these Proceedings reflects the choice of these topics. The section on commutative rings was intended to celebrate the 30-year anniversary of the publication of Robert Gilmer's monograph "Multiplicative Ideal Theory". Indeed, Gilmer was one of the main speakers, and seven leading researchers in commutative ring theory gave survey talks on the development of the subject in the last 30 years. A declared goal of the conference was to bring together mathematicians working in different areas of algebra to make evident the connections and interactions among these areas. The editors believe that these Proceedings reflect the success of the conference in achieving this goal, and we trust that the reader will find confirmation of this Additives Galois Theory of Modules R. Abraham and P. Schultz Finitely Generated and Cogenerated QD Groups U. Albrecht and B. Wickless Direct Limits of Modules of Finite Projective Dimension L. Angeleri Hugel and J. Trlifaj Classification of a Class of Almost Completely Decomposable Groups E. Blagoveshchenskaya A Polynomial Ring Sampler J. W. Brewer The Picard Group of the Ring of Integer-valued Polynomials on a Valuation Domain J-L. Chabert A Note on Cotilting Modules and Generalized Morita Duality R. R. Colby, R. Colpi, and K. R. Fuller Dualities Induced by Cotilting Bimodules R. Colpi Symmetries and Asymmetries for Cotilting Bimodules G D'Este A Constructive Solution to the Base Change Decomposition Problem in B(1)-groups C. De Vivo and C. Metilli On a Property of the Adele Ring of the Rationals D. Dikranjan and U. Zannier On a Strong Going-between, Going-down, and their Universalizations D.E. Dobbs and G. Picavet Factorization of Divosorial Ideals in a Generalized Krull Domain S. El Baghdadi Divisorial Multiplication Rings J. Escoriza and B. Torrecillas Global Deformations of Lie Algebras A. Fialowski.