Algebra and number theory : proceedings of a conference held in Fez, Morocco / edited by M'hammed Boulagouaz, Jean-Pierre Tignol.

Format:

Book

Contributor:

Boulagouaz, M'hammed, 1955-

Tignol, Jean-Pierre

Alumni and Friends Memorial Book Fund.

Series:

Lecture notes in pure and applied mathematics ; v. 208.

Lecture notes in pure and applied mathematics ; v. 208

Language:

English

Subjects (All):

Algebra--Congresses.

Algebra.

Number theory--Congresses.

Number theory.

Genre:

Conference papers and proceedings.

Physical Description:

x, 286 pages ; 26 cm.

Place of Publication:

New York : M. Dekker, [2000]

Summary:

This comprehensive reference demonstrates the key manipulations surrounding Brauer groups, graded rings, group representations, ideal classes of number fields, p-adic differential equations, and rationality problems of invariant fields -- displaying an extraordinary command of the most advanced methods in current algebra. Written by leading algebraists at work in the field today, Algebra and Number Theory analyzes modules, automorphisms, and the notion of gr-coherence...showcases graded multiplication rings, Dedekind rings, regular and noetherian V-rings, and semi-local rings ...illuminates the relationship between analoid sets and analytic functions...examines new theoretical aspects of cohomology, nonrational fields, graded coalgebras, and decomposition of orthogonal involutions...highlights Galois groups and the Galois correspondence theorem...investigates generic abelian crossed products...explores uses of differential modules and the Robba condition ...introduces the notion of orbital group actions on algebraic varieties...addresses quantum groups as Hopf algebras associated with variants of universal enveloping algebras...explains the theory of graded field extensions...and more. Containing over 300 references, Algebra and Number Theory is an ideal resource for pure and applied mathematicians, algebraists, number theorists, and upper-level undergraduate and graduate students in these disciplines.

Contents:

FP-gr-Injective Modules and gr-FC-Rings / M. J. Asensio, J. A. Lopez Ramos, B. Torrecillas 1

Capitulation of the 2-Ideal Classes of Q([radical]p[subscript 1]p[subscript 2], i) Where p[subscript 1] and p[subscript 2] Are Primes Such That p[subscript 1] [identical with] 1 (mod 8), p[subscript 2] [identical with] 5 (mod 8) and (p[subscript 1] / p[subscript 2]) = -1 / Abdelmalek Azizi 13

An Introduction to the Galois Theory for Graded Fields / M'hammed Boulagouaz 21

Generic Abelian Crossed Products and Graded Division Algebras / M'hammed Boulagouaz, Karim Mounirh 33

Strictly Analytic p-adic Functions / Kamal Boussaf 49

The Brauer-Long Group Revisited: The Multiplication Rules / S. Caenepeel 61

On Leopoldt's Index and a "Special" Class Number of Real Cyclic Extensions / M. E. Charkani 87

The Coradical Filtration for Some Quantum Groups / William Chin 95

p-adic Differential Equations / G. Christol, Z. Mebkhout 105

Orbitality and Vector Bundles / M. Daoudi 117

Multiplication Graded Rings / Jose Escoriza, Blas Torrecillas 127

Linear and Monomial Automorphisms of Fields of Rational Functions: Some Elementary Issues / Mowaffaq Hajja 137

A Dual Notion of CS-Modules Generalization / A. Idelhadj, R. Tribak 149

Socle-Fine Characterization of Dedekind and Regular Rings / A. Idelhadj, A. Yahya 157

Integral Representations of Some p-Groups / Ming-Chang Kang 165

Derivatives of Abstract Analytic Elements / Nicolas Mainetti 173

Irregular p-adic Linear Differential Equations / S. Remmal, G. Christol 195

The Brauer Group of Multiplicative Invariant Fields / David J. Saltman 207

The Brauer Group of the Centers of Generic Division Algebras / David J. Saltman 227

A Nonrational Field, Answering a Question of Hajja / David J. Saltman 263

Quadratic Pairs on Biquaternion Algebras / Jean-Pierre Tignol 273.

Notes:

"This volume presents the proceedings of the Colloque International d'Algèbre et Théorie des Nombres ..."--P. iii.

Includes bibliographical references.

Local Notes:

Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.

ISBN:

0824703413

OCLC:

42643562