Among all areas of mathematics, algebra is one of the best suited to find applications within the frame of our booming technological society. The thirty-eight articles in this volume encompass the proceedings of the International Conference on Algebra and Its Applications (Athens, OH, 1999), which explored the applications and interplay among the disciplines of ring theory, linear algebra, and coding theory. The presentations collected here reflect the dialogue between mathematicians involved in theoretical aspects of algebra and mathematicians involved in solving problems where state-of-the-art research tools may be used and applied. This ""Contemporary Mathematics"" series volume communicates the potential for collaboration among those interested in exploring the wealth of applications for abstract algebra in fields such as information and coding. The expository papers would serve well as supplemental reading in graduate seminars.
Isomorphisms between infinite matrix rings: A survey by G. Abrams and J. J. Simon The double infinite chain condition and generalized deviations of posets and modules by T. Albu and M. L. Teply Minors of some matrices associated with a tree by R. B. Bapat and D. M. Kulkarni On quasi-Baer rings by G. F. Birkenmeier, J. Y. Kim, and J. K. Park Functional identities: A survey by M. Bresar The Grothendieck group and the extensional structure of Noetherian module categories by G. Brookfield Some non-classical finiteness conditions of modules by J. Dauns and Y. Zhou Free modules obtained by means of infinite direct products by G. D'Este Gorenstein injective, projective, and flat dimensions over Cohen-Macaulay rings by E. E. Enochs and O. M. G. Jenda Projective modules over semilocal rings by A. Facchini and D. Herbera Determinantal inequalities: Ancient history and recent advances by S. M. Fallat and C. R. Johnson Ring extensions and duality by K. R. Fuller Some properties of tensor-idempotent rings by J. L. Garcia and L. Marin The graded version of Goldie's theorem by K. R. Goodearl and J. T. Stafford On Artinian and Noetherian projective lattice geometries by M. Greferath The phantom menace in representation theory by B. Huisgen-Zimmermann Separability and Hopf algebras by L. Kadison and A. A. Stolin Quadratic residue codes over the integers modulo $q^m$ by P. Kanwar Characterizations of right perfect rings by $\oplus$-supplemented modules by D. Keskin The adjacency matrix of a directed graph over the Grassmann algebra by P. Kortesi and J. Szigeti On Artinian modules over hyperfinite groups by L. A. Kurdachenko and I. Ya. Subbotin Principal one-sided ideals in Ore polynomial rings by T. Y. Lam and A. Leroy Modules over hereditary Noetherian prime rings (Survey) by L. S. Levy Prime elements of birational extensions of a Noetherian UFD by A. Li On the splitting of the dual Goldie torsion theory by C. Lomp The Soules approach to the inverse eigenvalue problem for nonnegative symmetric matrices of order $n \leq 5$ by J. J. McDonald and M. Neumann Harmonic analysis on finite rings and applications by C. J. Moreno A lattice invariant for modules, II by B. L. Osofsky Modules having $^*$-radical by A. C. Ozcan The ""generalized class group"" of a left Noetherian ring by C. J. Pappacena Indecomposable decompositions of $\aleph$-$\Sigma$-CS-modules by J. L. Gomez Pardo and P. A. Guil Asensio The multiplicative group of a division algebra of degree 5 and Wedderburn's factorization theorem by L. H. Rowen and Y. Segev Modules which are self-injective relative to closed submodules by C. Santa-Clara and P. F. Smith On $r$-fold complete weight enumerators of $r$ linear codes by I. Siap and D. K. Ray-Chaudhuri Levels of quotient rings of rings of continuous functions by A. I. Singh and M. A. Swardson Commutative domains whose finitely generated projective modules have an injectivity property by P. F. Smith Decompositions of modules and comodules by R. Wisbauer Density for polyform modules by J. M. Zelmanowitz.