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Abelian groups, rings, modules, and homological algebra /   Publication : [S.l.] Chapman and Hall/CRC 2006 . 360 p. , About the book… In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the participants of these talks along with contributions from other veteran researchers who were unable to attend. These papers reflect many of the current topics in Abelian Groups, Commutative Algebra, Commutative Rings, Group Theory, Homological Algebra, Lie Algebras, and Module Theory. Accessible even to beginning mathematicians, many of these articles suggest problems and programs for future study. This volume is an outstanding addition to the literature and a valuable handbook for beginning as well as seasoned researchers in Algebra. about the editors… H. PAT GOETERS completed his undergraduate studies in mathematics and computer science at Southern Connecticut State University and received his Ph.D. in 1984 from the University of Connecticut under the supervision of William J. Wickless. After spending one year in a post-doctoral position in Wesleyan University under the tutelage of James D. Reid, Goeters was invited for a tenure track position in Auburn University by Ulrich F. Albrecht. Soon afterwards, William Ullery and Overtoun Jenda were hired, and so began a lively Algebra group. OVERTOUN M. G. JENDA received his bachelor's degree in Mathematics from Chancellor College, the University of Malawi. He moved to the U.S. 1977 to pursue graduate studies at University of Kentucky, earning his Ph.D. in 1981 under the supervision of Professor Edgar Enochs. He then returned to Chancellor College, where he was a lecturer (assistant professor) for three years. He moved to the University of Botswana for another three-year stint as a lecturer before moving back to the University of Kentucky as a visiting assistant professor in 1987. In 1988, he joined the Algebra research group at Auburn University. 26 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),
Classes of modules par Dauns,, John. Publication : [S.l.] Chapman and Hall/CRC 2006 . 232 p. , Because traditional ring theory places restrictive hypotheses on all submodules of a module, its results apply only to small classes of already well understood examples. Often, modules with infinite Goldie dimension have finite-type dimension, making them amenable to use with type dimension, but not Goldie dimension. By working with natural classes and type submodules (TS), Classes of Modules develops the foundations and tools for the next generation of ring and module theory. It shows how to achieve positive results by placing restrictive hypotheses on a small subset of the complement submodules, Furthermore, it explains the existence of various direct sum decompositions merely as special cases of type direct sum decompositions. Carefully developing the foundations of the subject, the authors begin by providing background on the terminology and introducing the different module classes. The modules classes consist of torsion, torsion-free, s[M], natural, and prenatural. They expand the discussion by exploring advanced theorems and new classes, such as new chain conditions, TS-module theory, and the lattice of prenatural classes of right R-modules, which contains many of the previously used lattices of module classes. The book finishes with a study of the Boolean ideal lattice of a ring. Through the novel concepts presented, Classes of Modules provides a new, unexplored direction to take in ring and module theory. 25 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Difference methods for singular perturbation problems par Shishkin, Grigory I. Publication : [S.l.] Chapman and Hall/CRC 2008 . 408 p. ,   Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε -uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical methods. The first part of the book explores boundary value problems for elliptic and parabolic reaction-diffusion and convection-diffusion equations in n -dimensional domains with smooth and piecewise-smooth boundaries. The authors develop a technique for constructing and justifying ε uniformly convergent difference schemes for boundary value problems with fewer restrictions on the problem data. Containing information published mainly in the last four years, the second section focuses on problems with boundary layers and additional singularities generated by nonsmooth data, unboundedness of the domain, and the perturbation vector parameter. This part also studies both the solution and its derivatives with errors that are independent of the perturbation parameters. Co-authored by the creator of the Shishkin mesh, this book presents a systematic, detailed development of approaches to construct ε uniformly convergent finite difference schemes for broad classes of singularly perturbed boundary value problems. 24 cm. Date : 2008 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Differential equations, dynamical systems, and an introduction to chaos, second edition / par Devaney,, Robert. Publication : [S.l.] : Academic Press, 2003 . 425 p. ; , Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field's Medal for his work in dynamical systems. * Developed by award-winning researchers and authors * Provides a rigorous yet accessible introduction to differential equations and dynamical systems * Includes bifurcation theory throughout * Contains numerous explorations for students to embark upon NEW IN THIS EDITION * New contemporary material and updated applications * Revisions throughout the text, including simplification of many theorem hypotheses * Many new figures and illustrations * Simplified treatment of linear algebra * Detailed discussion of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor * Increased coverage of discrete dynamical systems. 23 cm. Date : 2003 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Noncommutative distributions : unitary representation of gauge groups and algebras par Albeverio, Sergio. Publication : [S.l.] M. Dekker, cop. 1993 . 190 p. , Covering important aspects of the theory of unitary representations of nuclear Lie groups, this self-contained reference presents the general theory of energy representations and addresses various extensions of path groups and algebras.;Requiring only a general knowledge of the theory of unitary representations, topological groups and elementary stochastic analysis, Noncommutative Distributions: examines a theory of noncommutative distributions as irreducible unitary representations of groups of mappings from a manifold into a Lie group, with applications to gauge-field theories; describes the energy representation when the target Lie group G is compact; discusses representations of G-valued jet bundles when G is not necessarily compact; and supplies a synthesis of deep results on quasi-simple Lie algebras.;Providing over 200 bibliographic citations, drawings, tables, and equations, Noncommutative Distributions is intended for research mathematicians and theoretical and mathematical physicists studying current algebras, the representation theory of Lie groups, and quantum field theory, and graduate students in these disciplines. 24 cm. Date : 1993 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Simple extensions with the minimum degree relations of integral domains par Oda, Susumu. Publication : [S.l.] Chapman and Hall/CRC 2007 . 296 p. , Although there are many types of ring extensions, simple extensions have yet to be thoroughly explored in one book. Covering an understudied aspect of commutative algebra, Simple Extensions with the Minimum Degree Relations of Integral Domains presents a comprehensive treatment of various simple extensions and their properties. In particular, it examines several properties of simple ring extensions of Noetherian integral domains. As experts who have been studying this field for over a decade, the authors present many arguments that they have developed themselves, mainly exploring anti-integral, super-primitive, and ultra-primitive extensions. Within this framework, they study certain properties, such as flatness, integrality, and unramifiedness. Some of the topics discussed include Sharma polynomials, vanishing points, Noetherian domains, denominator ideals, unit groups, and polynomial rings. Presenting a complete treatment of each topic, Simple Extensions with the Minimum Degree Relations of Integral Domains serves as an ideal resource for graduate students and researchers involved in the area of commutative algebra. 23 cm. Date : 2007 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Algebra / par Grove, Larry C. Publication : . 1 online resource (xiii, 299 pages) : Disponibilité :  http://www.sciencedirect.com/science/book/9780123046208,  http://www.sciencedirect.com/science/publication?issn=00798169&volume=110,

Multiplicative theory of ideals / par Larsen, Max D. Publication : . 1 online resource (xiv, 298 pages) Disponibilité :  http://www.sciencedirect.com/science/book/9780124368507,  http://www.sciencedirect.com/science/publication?issn=00798169&volume=43,

Banach algebra techniques in operator theory / par Douglas, Ronald G. Publication : . 1 online resource (xvi, 216 pages) Disponibilité :  http://www.sciencedirect.com/science/book/9780122213502,  http://www.sciencedirect.com/science/publication?issn=00798169&volume=49,

Differential equations, dynamical systems, and linear algebra / par Hirsch, Morris W., Publication : . 1 online resource (xi, 358 pages) : Disponibilité :  http://www.sciencedirect.com/science/book/9780123495501,  http://www.sciencedirect.com/science/publication?issn=00798169&volume=60,

An introduction to homological algebra / par Rotman, Joseph J., Publication : . 1 online resource (xi, 376 pages) : Disponibilité :  http://www.sciencedirect.com/science/book/9780125992503,  http://www.sciencedirect.com/science/publication?issn=00798169&volume=85,

Infinite crossed products / par Passman, Donald S., Publication : . 1 online resource (xii, 468 pages) : Disponibilité :  http://www.sciencedirect.com/science/book/9780125463904,  http://www.sciencedirect.com/science/publication?issn=00798169&volume=135,

A theory of sets / par Morse, Anthony P. Publication : . 1 online resource (xxxi, 130 pages) Disponibilité :  http://www.sciencedirect.com/science/book/9780123745675,  http://www.sciencedirect.com/science/publication?issn=00798169&volume=18,

Ring theory / par Behrens, Ernst-August. Publication : . 1 online resource (vii, 320 pages) Disponibilité :  http://www.sciencedirect.com/science/book/9780120852505,  http://www.sciencedirect.com/science/publication?issn=00798169&volume=44,

Introduction to Lie groups and Lie algebras / par Sagle, Arthur A. Publication : . 1 online resource (ix, 361 pages) Disponibilité :  http://www.sciencedirect.com/science/book/9780126145502,  http://www.sciencedirect.com/science/publication?issn=00798169&volume=51,

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