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Quasi-Frobenius Ringsby W. K. Nicholson; M. F. Yousif; B. Bollobas; W. Fulton; A. Katok; F. Kirwan; P. Sarnak
Cambridge University Press 2003; US$ 107.00A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian. While the present extent of the theory of these rings is vast, this book provides a self-contained account at a level allowing researchers and graduate students to gain entry to the field. more...
Corings and Comodulesby Tomasz Brzezinski; Robert Wisbauer; J. W. S. Cassels
Cambridge University Press 2003; US$ 70.00This is the first extensive treatment of the theory of corings and their comodules. In the first part, the module-theoretic aspects of coalgebras over commutative rings are described. Corings are then defined as coalgebras over non-commutative rings. Topics covered include module-theoretic aspects of corings, such as the relation of comodules to special subcategories of the category of modules (sigma-type categories), connections between corings and extensions of rings, properties of new examples of corings associated to entwining structures, generalisations of bialgebras such as bialgebroids and weak bialgebras, and the appearance of corings in non-commutative geometry. more...
Frobenius Algebras and 2-D Topological Quantum Field Theoriesby Joachim Kock; C. M. Series
Cambridge University Press 2003; US$ 45.00Proves striking results connecting topology and algebra and shows how the result fits into a more general pattern. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques. There are numerous exercises and examples making the book suitable for teaching. more...
Nearrings and Nearfieldsby Hubert Kiechle; Alexander Kreuzer; Momme Johs Thomsen
Springer 2005; US$ 119.00The present volume is the Proceedings of the 18th International Conference on Nearrings and Nearfields held at the Helmut-Schmidt-Universität, Universität der Bundeswehr Hamburg, from July 27 ? August 3, 2003. It contains the written versions of the lectures by the five invited speakers. These concern recent developments of planar nearrings, nearrings of mappings, group nearrings and loop-nearrings. One of them is a long and very substantial research paper "The Z-Constrained Conjecture". They are followed by 13 contributions reflecting the diversity of the subject of nearrings and related structures. Besides the purely algebraic structure theory these papers show many connections of nearring theory with group theory, combinatorics, geometries,... more...
Noetherian Semigroup Algebrasby Eric Jespers; Jan Okninski
Springer 2007; US$ 95.00Within the last decade, semigroup theoretical methods have occurred naturally in many aspects of ring theory, algebraic combinatorics, representation theory and their applications. In particular, motivated by noncommutative geometry and the theory of quantum groups, there is a growing interest in the class of semigroup algebras and their deformations. This work presents a comprehensive treatment of the main results and methods of the theory of Noetherian semigroup algebras. These general results are then applied and illustrated in the context of important classes of algebras that arise in a variety of areas and have been recently intensively studied. Several concrete constructions are described in full detail, in particular intriguing classes... more...
Elements of the Representation Theory of Associative Algebrasby Ibrahim Assem; Andrzej Skowronski; Daniel Simson
Cambridge University Press 2006; US$ 45.00Provides an elementary but up-to-date introduction to the representation theory of algebras. more...
Elements of the Representation Theory of Associative Algebrasby Daniel Simson; Andrzej Skowronski
Cambridge University Press 2007; US$ 56.00Volume two of this modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field more...
Elements of the Representation Theory of Associative Algebrasby Daniel Simson; Andrzej Skowronski
Cambridge University Press 2007; US$ 56.00Volume three of this modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. more...
Near-Rings and Near-Fieldsby G. Betsch
Elsevier 1987; US$ 223.00Most topics in near-ring and near-field theory are treated here, along with an extensive introduction to the theory. There are two invited lectures: ``Non-Commutative Geometry, Near-Rings and Near-Fields'' which indicates the relevance of near-rings and near-fields for geometry, while ``Pseudo-Finite Near-Fields'' shows the impressive power of model theoretic methods. The remaining papers cover such topics as D.G. near-rings, radical theory, KT-near-fields, matrix near-rings, and applications to systems theory. more...
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Springer 2007; US$ 49.95The theory of functional identities (FIs) is a relatively new one - the first results were published at the beginning of the 1990s, and this is the first book on this subject. An FI can be informally described as an identical relation involving arbitrary elements in an associative ring together with arbitrary (unknown) functions. The goal of the general FI theory is to describe these functions, or, when this is not possible, to describe the structure of the ring admitting the FI in question. This abstract theory has turned out to be a powerful tool for solving a variety of problems in ring theory, Lie algebras, Jordan algebras, linear algebra, and operator theory. The book is divided into three parts. Part I is an introductory one. Part II... more...
