to Group Rings by Cesar Polcino Milies Instituto de Matematica e Estatistica, Universidade de sao Paulo, sao Paulo, Brasil and Sudarshan K. Sehgal Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton. Canada SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A c.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4020-0239-7 ISBN 978-94-010-0405-3 (eBook) DOI 10.1007/978-94-010-0405-3 Printed an acid-free paper AII Rights Reserved (c) 2002 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in...
to Group Rings by Cesar Polcino Milies Instituto de Matematica e Estatistica, Universidade de sao Paulo, sao Paulo, Brasil and Sudarshan K. Sehgal Dep...
Group cohomology has a rich history that goes back a century or more. Its origins are rooted in investigations of group theory and num- ber theory, and it grew into an integral component of algebraic topology. In the last thirty years, group cohomology has developed a powerful con- nection with finite group representations. Unlike the early applications which were primarily concerned with cohomology in low degrees, the in- teractions with representation theory involve cohomology rings and the geometry of spectra over these rings. It is this connection to represen- tation theory that we take...
Group cohomology has a rich history that goes back a century or more. Its origins are rooted in investigations of group theory and num- ber theory, an...
The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications.
The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on ...
Every Abelian group can be related to an associative ring with an identity element, the ring of all its endomorphisms. Recently the theory of endomor- phism rings of Abelian groups has become a rapidly developing area of algebra. On the one hand, it can be considered as a part of the theory of Abelian groups; on the other hand, the theory can be considered as a branch of the theory of endomorphism rings of modules and the representation theory of rings. There are several reasons for studying endomorphism rings of Abelian groups: first, it makes it possible to acquire additional information...
Every Abelian group can be related to an associative ring with an identity element, the ring of all its endomorphisms. Recently the theory of endomor-...
The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves cf. 148], 149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . ., m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _...
The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's wo...
This monograph is devoted to a new class of non-commutative rings, skew Poincaré–Birkhoff–Witt (PBW) extensions. Beginning with the basic definitions and ring-module theoretic/homological properties, it goes on to investigate finitely generated projective modules over skew PBW extensions from a matrix point of view. To make this theory constructive, the theory of Gröbner bases of left (right) ideals and modules for bijective skew PBW extensions is developed. For example, syzygies and the Ext and Tor modules over these rings are computed. Finally, applications to some key...
This monograph is devoted to a new class of non-commutative rings, skew Poincaré–Birkhoff–Witt (PBW) extensions. Beginning with the bas...
This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras, such as algebras of representative functions on groups and enveloping algebras of Lie algebras, as explored in the works of Borel, Cartier, Hopf and others in the 1940s and 50s.
The modern and systematic treatment uses the approach of natural operations, illuminating the structure of Hopf algebras by means of their endomorphisms and their combinatorics. Emphasizing notions such as pseudo-coproducts, characteristic endomorphisms, descent...
This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras...
This book offers an original introduction to the representation theory of algebras, suitable for beginning researchers in algebra. It includes many results and techniques not usually covered in introductory books, some of which appear here for the first time in book form.
The exposition employs methods from linear algebra (spectral methods and quadratic forms), as well as categorical and homological methods (module categories, Galois coverings, Hochschild cohomology) to present classical aspects of ring theory under new light. This includes topics such as rings...
This book offers an original introduction to the representation theory of algebras, suitable for beginning researchers in algebra. It includes ma...
