Algebra and Its Applications: (Contemporary Mathematics)

This volume consists of contributions by speakers at a Conference on Algebra and its Applications that took place in Athens, Ohio, in March of 2005. It provides a snapshot of the diversity of themes and applications that interest algebraists today. The papers in this volume include some of the latest results in the theory of modules, noncommutative rings, representation theory, matrix theory, linear algebra over noncommutative rings, cryptography, error-correcting codes over finite rings, and projective-geometry codes, as well as expository articles that will provide algebraists and other mathematicians, including graduate students, with an accessible introduction to areas outside their own expertise. The book will serve both the specialist looking for the latest result and the novice seeking an accessible reference for some of the ideas and results presented here.

Table of Contents:
On countably $\Sigma$-CS modules by A. N. Alahmadi, H. S. Al-Hazmi, and P. A. Guil Asensio Moduli spaces of graded representations of finite dimensional algebras by E. Babson, B. Huisgen-Zimmermann, and R. Thomas An essential extension with nonisomorphic ring structures by G. F. Birkenmeier, J. K. Park, and S. T. Rizvi Supplemented principal ideals by V. Camillo and S. Lima Some properties of rings reflected in infinite matrix rings by V. Camillo and J. J. Simon Slender monoids by R. M. Dimitric Multivariable public key crytosystems by J. Ding and D. Schmidt Repeated-root constacyclic codes of length $2^s$ over $\mathbb{Z}_{2^a}$ by H. Q. Dinh Contravariant finiteness and pure semisimple rings by N. V. Dung A characterization of additive categories with the Krull-Schmidt property by A. Facchini A Dixmier-Moeglin equivalence for Poisson algebras with torus actions by K. R. Goodearl Pure-injectivity in the category of flat modules by P. A. Guil Asensio and I. Herzog Eigenvalues, multiplicities and graphs by C. R. Johnson, A. L. Duarte, C. M. Saiago, and D. Sher Closure of matrix classes under Schur complementation, including singularities by C. R. Johnson and R. L. Smith Sums of alternating matrices and invertible matrices by T. Y. Lam and R. G. Swan Internal exchange rings by S. H. Mohamed Representations of $\sigma$-complete MV-algebras and their associated Dedekind $\sigma$-complete $\ell$-groups by D. Mundici Noncommutative linear algebra by B. L. Osofsky The moduli space of three-dimensional Lie algebras by C. Otto and M. Penkava Questions related to Koethe's nil ideal problem by E. R. Puczylowski Bounds on the pseudo-weight of minimal pseudo-codewords of projective geometry codes by R. Smarandache and M. Wauer On Galois extensions with automorphism group as Galois group by G. Szeto and L. Xue A *-Litoff theorem for associative pairs by M. Tocon Open problems by J. Ding, D. Mundici, D. S. Passman, J. B. Srivastava, and L. Vas.