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Equivalence and Duality for Module Categories with Tilting and Cotilting for Rings
Cambridge University Press 2004; US$ 71.00This book provides a unified and innovative approach to much of the theories of equivalence and duality between categories of modules that has transpired over the last 45 years. The authors discuss the relationships between categories of modules over a pair of rings that are induced by both covariant and contravariant representable functors, in particular... more...
Introductory Algebraic Number Theory
Cambridge University Press 2003; US$ 49.00An introduction to algebraic number theory for senior undergraduates and beginning graduate students in mathematics. It includes numerous examples, and references to further reading and to biographies of mathematicians who have contributed to the development of the subject. Includes over 320 exercises, and an extensive index. more...
Non-Unique Factorizations
CRC Press 2006; US$ 149.95Geroldinger and Halter-Koch, both professors of mathematics at Karl Franzens University in Austria, outline the present state of the theory of non-unique factorizations and discuss related algebraic, combinatorial, and analytic fundamentals. The introductory chapter is accessible to readers with background in standard basic algebra. Coverage then m more...
The Square Root of 2
Springer-Verlag New York Inc 2006; US$ 19.99The square root of 2 is a fascinating number, if a little less famous than such mathematical stars as pi, the number e, the golden ratio, or the square root of 1. This book shows why v2 is an important number, and how, in puzzling out its special qualities, mathematicians gained insights into the illusive nature of irrational numbers. more...
Free Ideal Rings and Localization in General Rings
Cambridge University Press 2006; US$ 181.00This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras, and there is also a full account of localization. Each chapter has a number of exercises plus open problems and historical notes. more...
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De Gruyter 2006; US$ 224.00This monograph provides a thorough treatment of module theory, a subfield of algebra. The authors develop an approximation theory as well as realization theorems and present some of its recent applications, notably to infinite-dimensional combinatorics and model theory. The book is devoted to graduate students interested in algebra as well as to experts... more...
Certain Number-Theoretic Episodes In Algebra
CRC Press 2006; US$ 179.95There are many intersections between the fields of algebra and number theory, and in certain cases there exist explicit algebraic analogues of theorems from number theory. Presenting the tools needed to explore these linkages, this reference explains the conceptual foundations of commutative algebra arising from number theory. more...
Advances In Ring Theory - Proceedings Of The 4th China-japan-korea International Conference
World Scientific Publishing Company 2005; US$ 127.00The selected papers in this volume cover all the most important areas of ring theory and module theory such as classical ring theory, representation theory, the theory of quantum groups, the theory of Hopf algebras, the theory of Lie algebras and Abelian group theory. The review articles, written by specialists, provide an excellent overview of the... more...
Problems in Algebraic Number Theory
Springer-Verlag New York Inc 2006; US$ 59.99Arranged to present the evolution of concepts and ideas of the subject, this is a collection of about 500 problems in algebraic number theory. Containing solved problems, it is designed for students with the usual background of undergraduate algebra. more...
Lifting Modules
Springer 2006; US$ 69.95Provides a study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules. This book introduces small submodules, the radical, variations on projectivity, and hollow dimension. It considers preradicals and torsion theories, decompositions of modules, supplements in modules, and lifting modules. more...
