Algebra and Its Applications

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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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.

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Editorial Reviews

Booknews
To explore the applications that exist for abstract algebra in fields such as information and coding, mathematicians gathered for a March 1999 international conference in Athens, Ohio. In 38 papers, they discuss such aspects as the double infinite chain condition and generalized deviations of posets and modules, some non-classical finiteness conditions of modules, projective modules over semilocal rings, the phantom menace in representation theory, splitting the dual Goldie torsion theory, harmonic analysis on finite rings and applications, modules that are self-injected relative to closed submolecules, levels of quotient rings of continuous functions, and density for polyform modules. There is no index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Preface
Isomorphisms between infinite matrix rings: A survey 1
The double infinite chain condition and generalized deviations of posets and modules 13
Minors of some matrices associated with a tree 45
On quasi-Baer rings 67
Functional identities: A survey 93
The Grothendieck group and the extensional structure of Noetherian module categories 111
Some non-classical finiteness conditions of modules 133
Free modules obtained by means of infinite direct products 161
Gorenstein injective, projective, and flat dimensions over Cohen-Macaulay rings 175
Projective modules over semilocal rings 181
Determinantal inequalities: Ancient history and recent advances 199
Ring extensions and duality 213
Some properties of tensor-idempotent rings 223
The graded version of Goldie's theorem 237
On Artinian and Noetherian projective lattice geometries 241
The phantom menace in representation theory 247
Separability and Hopf algebras 279
Quadratic residue codes over the integers modulo q[superscript m] 299
Characterizations of right perfect rings by [actual symbol not reproducible]-supplemented modules 313
The adjacency matrix of a directed graph over the Grassmann algebra 319
On Artinian modules over hyperfinite groups 323
Principal one-sided ideals in Ore polynomial rings 333
Modules over hereditary Noetherian prime rings (Survey) 353
Prime elements of birational extensions of a Noetherian UFD 371
On the splitting of the dual Goldie torsion theory 377
The Soules approach to the inverse eigenvalue problem for nonnegative symmetric matrices of order n[is equal to or less than]5 387
Harmonic analysis on finite rings and applications 409
A lattice invariant for modules, II 431
Modules having [superscript *]-radical 439
The "generalized class group" of a left Noetherian ring 451
Indecomposable decompositions of [actual symbol not reproducible]-[Sigma]-CS-modules 467
The multiplicative group of a division algebra of degree 5 and Wedderburn's factorization theorem 475
Modules which are self-injective relative to closed submodules 487
On r-fold complete weight enumerators of r linear codes 501
Levels of quotient rings of rings of continuous functions 515
Commutative domains whose finitely generated projective modules have an injectivity property 529
Decompositions of modules and comodules 547
Density for polyform modules 563
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