eBook ISBN:  9780821878491 
Product Code:  CONM/259.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821878491 
Product Code:  CONM/259.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 259; 2000; 569 ppMSC: Primary 15; 16; 94
Among all areas of mathematics, algebra is one of the best suited to find applications within the frame of our booming technological society. The thirtyeight 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 stateoftheart 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.
ReadershipAdvanced graduate students and researchers in ring theory, linear algebra, and algebraic coding theory.

Table of Contents

Articles

Gene Abrams and Juan Jacobo Simón — Isomorphisms between infinite matrix rings: a survey [ MR 1778492 ]

Toma Albu and Mark L. Teply — The double infinite chain condition and generalized deviations of posets and modules [ MR 1778493 ]

R. B. Bapat and Devadatta M. Kulkarni — Minors of some matrices associated with a tree [ MR 1778494 ]

Gary F. Birkenmeier, Jin Yong Kim and Jae Keol Park — On quasiBaer rings [ MR 1778495 ]

Matej Brešar — Functional identities: a survey [ MR 1778496 ]

Gary Brookfield — The Grothendieck group and the extensional structure of Noetherian module categories [ MR 1778497 ]

John Dauns and Yiqiang Zhou — Some nonclassical finiteness conditions of modules [ MR 1778498 ]

Gabriella D’Este — Free modules obtained by means of infinite direct products [ MR 1778499 ]

Edgar E. Enochs and Overtoun M. G. Jenda — Gorenstein injective, projective, and flat dimensions over CohenMacaulay rings [ MR 1778500 ]

Alberto Facchini and Dolors Herbera — Projective modules over semilocal rings [ MR 1778501 ]

Shaun M. Fallat and Charles R. Johnson — Determinantal inequalities: ancient history and recent advances [ MR 1778502 ]

Kent R. Fuller — Ring extensions and duality [ MR 1778503 ]

José Luis García and Leandro Marín — Some properties of tensoridempotent rings [ MR 1780523 ]

K. R. Goodearl and J. T. Stafford — The graded version of Goldie’s theorem [ MR 1780524 ]

Marcus Greferath — On Artinian and Noetherian projective lattice geometries [ MR 1780525 ]

Birge HuisgenZimmermann — The phantom menace in representation theory [ MR 1780526 ]

Lars Kadison and A. A. Stolin — Separability and Hopf algebras [ MR 1780527 ]

Pramod Kanwar — Quadratic residue codes over the integers modulo $q^m$ [ MR 1780528 ]

Derya Keskin — Characterizations of right perfect rings by $\oplus $supplemented modules [ MR 1780529 ]

Péter Körtesi and Jenő Szigeti — The adjacency matrix of a directed graph over the Grassmann algebra [ MR 1780530 ]

L. A. Kurdachenko and I. Ya. Subbotin — On Artinian modules over hyperfinite groups [ MR 1780531 ]

T. Y. Lam and André Leroy — Principal onesided ideals in Ore polynomial rings [ MR 1780532 ]

Lawrence S. Levy — Modules over hereditary Noetherian prime rings (survey) [ MR 1780533 ]

Aihua Li — Prime elements of birational extensions of a Noetherian UFD [ MR 1780534 ]

Christian Lomp — On the splitting of the dual Goldie torsion theory [ MR 1780535 ]

J. J. McDonald and M. Neumann — The Soules approach to the inverse eigenvalue problem for nonnegative symmetric matrices of order $n\leq 5$ [ MR 1780536 ]

Carlos Julio Moreno — Harmonic analysis on finite rings and applications [ MR 1780537 ]

Barbara L. Osofsky — A lattice invariant for modules. II [ MR 1780538 ]

A. Çiğdem Özcan — Modules having $*$radical [ MR 1780539 ]

Christopher J. Pappacena — The “generalized class group” of a left Noetherian ring [ MR 1780540 ]

José L. Gómez Pardo and Pedro A. Guil Asensio — Indecomposable decompositions of $\aleph $$\sum $CSmodules [ MR 1780541 ]

Louis H. Rowen and Yoav Segev — The multiplicative group of a division algebra of degree 5 and Wedderburn’s factorization theorem [ MR 1780542 ]

Catarina SantaClara and Patrick F. Smith — Modules which are selfinjective relative to closed submodules [ MR 1780543 ]

Irfan Siap and Dijen K. RayChaudhuri — On $r$fold complete weight enumerators of $r$ linear codes [ MR 1780544 ]

Ajit Iqbal Singh and Mary Anne Swardson — Levels of quotient rings of rings of continuous functions [ MR 1780545 ]

Patrick F. Smith — Commutative domains whose finitely generated projective modules have an injectivity property [ MR 1780546 ]

Robert Wisbauer — Decompositions of modules and comodules [ MR 1780547 ]

Julius M. Zelmanowitz — Density for polyform modules [ MR 1780548 ]


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

Articles

Gene Abrams and Juan Jacobo Simón — Isomorphisms between infinite matrix rings: a survey [ MR 1778492 ]

Toma Albu and Mark L. Teply — The double infinite chain condition and generalized deviations of posets and modules [ MR 1778493 ]

R. B. Bapat and Devadatta M. Kulkarni — Minors of some matrices associated with a tree [ MR 1778494 ]

Gary F. Birkenmeier, Jin Yong Kim and Jae Keol Park — On quasiBaer rings [ MR 1778495 ]

Matej Brešar — Functional identities: a survey [ MR 1778496 ]

Gary Brookfield — The Grothendieck group and the extensional structure of Noetherian module categories [ MR 1778497 ]

John Dauns and Yiqiang Zhou — Some nonclassical finiteness conditions of modules [ MR 1778498 ]

Gabriella D’Este — Free modules obtained by means of infinite direct products [ MR 1778499 ]

Edgar E. Enochs and Overtoun M. G. Jenda — Gorenstein injective, projective, and flat dimensions over CohenMacaulay rings [ MR 1778500 ]

Alberto Facchini and Dolors Herbera — Projective modules over semilocal rings [ MR 1778501 ]

Shaun M. Fallat and Charles R. Johnson — Determinantal inequalities: ancient history and recent advances [ MR 1778502 ]

Kent R. Fuller — Ring extensions and duality [ MR 1778503 ]

José Luis García and Leandro Marín — Some properties of tensoridempotent rings [ MR 1780523 ]

K. R. Goodearl and J. T. Stafford — The graded version of Goldie’s theorem [ MR 1780524 ]

Marcus Greferath — On Artinian and Noetherian projective lattice geometries [ MR 1780525 ]

Birge HuisgenZimmermann — The phantom menace in representation theory [ MR 1780526 ]

Lars Kadison and A. A. Stolin — Separability and Hopf algebras [ MR 1780527 ]

Pramod Kanwar — Quadratic residue codes over the integers modulo $q^m$ [ MR 1780528 ]

Derya Keskin — Characterizations of right perfect rings by $\oplus $supplemented modules [ MR 1780529 ]

Péter Körtesi and Jenő Szigeti — The adjacency matrix of a directed graph over the Grassmann algebra [ MR 1780530 ]

L. A. Kurdachenko and I. Ya. Subbotin — On Artinian modules over hyperfinite groups [ MR 1780531 ]

T. Y. Lam and André Leroy — Principal onesided ideals in Ore polynomial rings [ MR 1780532 ]

Lawrence S. Levy — Modules over hereditary Noetherian prime rings (survey) [ MR 1780533 ]

Aihua Li — Prime elements of birational extensions of a Noetherian UFD [ MR 1780534 ]

Christian Lomp — On the splitting of the dual Goldie torsion theory [ MR 1780535 ]

J. J. McDonald and M. Neumann — The Soules approach to the inverse eigenvalue problem for nonnegative symmetric matrices of order $n\leq 5$ [ MR 1780536 ]

Carlos Julio Moreno — Harmonic analysis on finite rings and applications [ MR 1780537 ]

Barbara L. Osofsky — A lattice invariant for modules. II [ MR 1780538 ]

A. Çiğdem Özcan — Modules having $*$radical [ MR 1780539 ]

Christopher J. Pappacena — The “generalized class group” of a left Noetherian ring [ MR 1780540 ]

José L. Gómez Pardo and Pedro A. Guil Asensio — Indecomposable decompositions of $\aleph $$\sum $CSmodules [ MR 1780541 ]

Louis H. Rowen and Yoav Segev — The multiplicative group of a division algebra of degree 5 and Wedderburn’s factorization theorem [ MR 1780542 ]

Catarina SantaClara and Patrick F. Smith — Modules which are selfinjective relative to closed submodules [ MR 1780543 ]

Irfan Siap and Dijen K. RayChaudhuri — On $r$fold complete weight enumerators of $r$ linear codes [ MR 1780544 ]

Ajit Iqbal Singh and Mary Anne Swardson — Levels of quotient rings of rings of continuous functions [ MR 1780545 ]

Patrick F. Smith — Commutative domains whose finitely generated projective modules have an injectivity property [ MR 1780546 ]

Robert Wisbauer — Decompositions of modules and comodules [ MR 1780547 ]

Julius M. Zelmanowitz — Density for polyform modules [ MR 1780548 ]