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Algebra and Its Applications
Edited by: D. V. Huynh, S. K. Jain, and S. R. López-Permouth, Ohio University, Athens, OH
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Contemporary Mathematics
2000; 569 pp; softcover
Volume: 259
ISBN-10: 0-8218-1950-X
ISBN-13: 978-0-8218-1950-0
List Price: US$126
Member Price: US$100.80
Order Code: CONM/259
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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.

Readership

Advanced graduate students and researchers in ring theory, linear algebra, and algebraic coding theory.

Table of Contents

  • G. Abrams and J. J. Simón -- Isomorphisms between infinite matrix rings: A survey
  • T. Albu and M. L. Teply -- The double infinite chain condition and generalized deviations of posets and modules
  • R. B. Bapat and D. M. Kulkarni -- Minors of some matrices associated with a tree
  • G. F. Birkenmeier, J. Y. Kim, and J. K. Park -- On quasi-Baer rings
  • M. Brešar -- Functional identities: A survey
  • G. Brookfield -- The Grothendieck group and the extensional structure of Noetherian module categories
  • J. Dauns and Y. Zhou -- Some non-classical finiteness conditions of modules
  • G. D'Este -- Free modules obtained by means of infinite direct products
  • E. E. Enochs and O. M. G. Jenda -- Gorenstein injective, projective, and flat dimensions over Cohen-Macaulay rings
  • A. Facchini and D. Herbera -- Projective modules over semilocal rings
  • S. M. Fallat and C. R. Johnson -- Determinantal inequalities: Ancient history and recent advances
  • K. R. Fuller -- Ring extensions and duality
  • J. L. García and L. Marín -- Some properties of tensor-idempotent rings
  • K. R. Goodearl and J. T. Stafford -- The graded version of Goldie's theorem
  • M. Greferath -- On Artinian and Noetherian projective lattice geometries
  • B. Huisgen-Zimmermann -- The phantom menace in representation theory
  • L. Kadison and A. A. Stolin -- Separability and Hopf algebras
  • P. Kanwar -- Quadratic residue codes over the integers modulo \(q^m\)
  • D. Keskin -- Characterizations of right perfect rings by \(\oplus\)-supplemented modules
  • P. Körtesi and J. Szigeti -- The adjacency matrix of a directed graph over the Grassmann algebra
  • L. A. Kurdachenko and I. Ya. Subbotin -- On Artinian modules over hyperfinite groups
  • T. Y. Lam and A. Leroy -- Principal one-sided ideals in Ore polynomial rings
  • L. S. Levy -- Modules over hereditary Noetherian prime rings (Survey)
  • A. Li -- Prime elements of birational extensions of a Noetherian UFD
  • C. Lomp -- On the splitting of the dual Goldie torsion theory
  • J. J. McDonald and M. Neumann -- The Soules approach to the inverse eigenvalue problem for nonnegative symmetric matrices of order \(n \leq 5\)
  • C. J. Moreno -- Harmonic analysis on finite rings and applications
  • B. L. Osofsky -- A lattice invariant for modules, II
  • A. Özcan -- Modules having \(^*\)-radical
  • C. J. Pappacena -- The "generalized class group" of a left Noetherian ring
  • J. L. Gómez Pardo and P. A. Guil Asensio -- Indecomposable decompositions of \(\aleph\)-\(\Sigma\)-CS-modules
  • L. H. Rowen and Y. Segev -- The multiplicative group of a division algebra of degree 5 and Wedderburn's factorization theorem
  • C. Santa-Clara and P. F. Smith -- Modules which are self-injective relative to closed submodules
  • I. Siap and D. K. Ray-Chaudhuri -- On \(r\)-fold complete weight enumerators of \(r\) linear codes
  • A. I. Singh and M. A. Swardson -- Levels of quotient rings of rings of continuous functions
  • P. F. Smith -- Commutative domains whose finitely generated projective modules have an injectivity property
  • R. Wisbauer -- Decompositions of modules and comodules
  • J. M. Zelmanowitz -- Density for polyform modules
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