**Contemporary Mathematics**

Volume: 259;
2000;
569 pp;
Softcover

MSC: Primary 15; 16; 94;

Print ISBN: 978-0-8218-1950-0

Product Code: CONM/259

List Price: $126.00

AMS Member Price: $100.80

MAA Member Price: $113.40

**Electronic ISBN: 978-0-8218-7849-1
Product Code: CONM/259.E**

List Price: $126.00

AMS Member Price: $100.80

MAA Member Price: $113.40

# Algebra and Its Applications

Share this page *Edited by *
*D. V. Huynh; S. K. Jain; S. R. López-Permouth*

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

## Algebra and Its Applications

- Contents vii8 free
- Preface xi12 free
- Isomorphisms between infinite matrix rings: A survey 114 free
- The double infinite chain condition and generalized deviations of posets and modules 1326
- Minors of some matrices associated with a tree 4558
- On quasi-Baer rings 6780
- Functional identities: A survey 93106
- The Grothendieck group and the extensional structure of Noetherian module categories 111124
- Some non-classical finiteness conditions of modules 133146
- Free modules obtained by means of infinite direct products 161174
- Gorenstein injective, projective, and flat dimensions over Cohen-Macaulay rings 175188
- Projective modules over semilocal rings 181194
- Determinantal inequalities: Ancient history and recent advances 199212
- Ring extensions and duality 213226
- Some properties of tensor-idempotent rings 223236
- The graded version of Goldie's theorem 237250
- On Artinian and Noetherian projective lattice geometries 241254
- The phantom menace in representation theory 247260
- Separability and Hopf algebras 279292
- Quadratic residue codes over the integers modulo qm 299312
- Characterizations of right perfect rings by ⊕supplemented modules 313326
- The adjacency matrix of a directed graph over the Grassmann algebra 319332
- On Artinian modules over hyperfinite groups 323336
- Principal one-sided ideals in Ore polynomial rings 333346
- Modules over hereditary Noetherian prime rings (Survey) 353366
- Prime elements of birational extensions of a Noetherian UFD 371384
- On the splitting of the dual Goldie torsion theory 377390
- The Soules approach to the inverse eigenvalue problem for nonnegative symmetric matrices of order n ≤ 5 387400
- Harmonic analysis on finite rings and applications 409422
- A lattice invariant for modules, II 431444
- Modules having *-radical 439452
- The "generalized class group" of a left Noetherian ring 451464
- Indecomposable decompositions of N-∑-CS-modules 467480
- The multiplicative group of a division algebra of degree 5 and Wedderburn's factorization theorem 475488
- Modules which are self-injective relative to closed submodules 487500
- On r-fold complete weight enumerators of r linear codes 501514
- Levels of quotient rings of rings of continuous functions 515528
- Commutative domains whose finitely generated projective modules have an injectivity property 529542
- Decompositions of modules and comodules 547560
- Density for polyform modules 563576