## Algebra and Its Applications: International Conference, Algebra and Its Applications, March 22-26, 2005, Ohio University, Athens, OhioChina) International Conference on Advances in Structural Dynamics (2000 : Hong Kong, D. V. Huynh, International Conference Algebra and Its Applications, Surender Kumar Jain, Sergio R. López-Permouth, S R Lopez-Permouth American Mathematical Soc., 2000 - 569 páginas 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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### Conteúdo

1 | |

13 | |

Minors of some matrices associated with a tree | 45 |

On quasiBaer rings | 67 |

A survey | 93 |

The Grothendieck group and the extensional structure of Noetherian module categories | 111 |

Some nonclassical finiteness conditions of modules | 133 |

Free modules obtained by means of infinite direct products | 161 |

On Artinian modules over hyperfinite groups | 323 |

Principal onesided 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 5 | 387 |

Harmonic analysis on finite rings and applications | 409 |

A lattice invariant for modules II | 431 |

Gorenstein injective projective and flat dimensions over CohenMacaulay rings | 175 |

Projective modules over semilocal rings | 181 |

Ancient history and recent advances | 199 |

Ring extensions and duality | 213 |

Some properties of tensoridempotent rings | 223 |

The graded version of Goldies 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 qm | 299 |

Characterizations of right perfect rings by supplemented modules | 313 |

The adjacency matrix of a directed graph over the Grassmann algebra | 319 |

Modules having radical | 439 |

The generalized class group of a left Noetherian ring | 451 |

Indecomposable decompositions of NCSmodules | 467 |

The multiplicative group of a division algebra of degree 5 and Wedderburns factorization theorem | 475 |

Modules which are selfinjective relative to closed submodules | 487 |

On rfold 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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### Termos e frases comuns

A-mod Amer Artinian artinian ring Baer ring commutative Corollary countable decomposition Dedekind defined definition denote direct sum direct summand domain dual element endomorphism exact sequence example exists extension factor Frobenius Go(R Gorenstein graph Hence hereditary homomorphism idempotent implies indecomposable inequality infinite matrix rings injective injective modules integer isomorphic k-algebra Krull dimension lattice left ideal left R-module Lemma linear M-injective M-singular M(R-Noeth Math matrix rings minimal Mod-R monic monoid Morita equivalent Noetherian ring nonnegative nonsingular nonzero notation Note order type polyform polynomial poset prime ideal prime rings projective module proof Proposition prove quadratic residue quasi-Baer ring quotient R-module R-Noeth resp result RFM(R right ideal right R-module satisfies self-c-injective semigroup semilocal semiprimary semiprime semisimple simple modules strongly separable subcategory subring subset Suppose symmetric Theorem torsion theory type direct sum weakly weight enumerator