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#### Problems in Algebraic Number Theory

Springer New York 2006; US$ 56.95Asking how one does mathematical research is like asking how a composer creates a masterpiece. No one really knows. However, it is a recognized fact that problem solving plays an important role in training the mind of a researcher. It would not be an exaggeration to say that the ability to do mathematical research lies essentially asking "well-posed"... more...

#### Almost Free Modules

Elsevier Science 2002; US$ 195.00This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This second edition is completely revised and udated to include major... more...

#### Lifting Modules

Birkhäuser Basel 2008; US$ 47.42Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. There is a certain asymmetry in this duality. While the theory of extending modules is well documented in monographs and text books, the purpose of our monograph is to provide a thorough study of supplements and projectivity... more...

#### Cyclotomic Fields and Zeta Values

Springer Berlin Heidelberg 2006; US$ 49.61Cyclotomic fields have always occupied a central place in number theory, and the so called "main conjecture" on cyclotomic fields is arguably the deepest and most beautiful theorem known about them. It is also the simplest example of a vast array of subsequent, unproven "main conjectures'' in modern arithmetic geometry involving the arithmetic behaviour... more...

#### Algebraische Zahlentheorie

Springer Berlin Heidelberg 2006; US$ 13.30Die algebraische Zahlentheorie ist eine der traditionsreichsten und gleichzeitig heute besonders aktuellen Grunddisziplinen der Mathematik. In dem vorliegenden Buch wird sie in einem ausführlichen und weitgefaßten Rahmen abgehandelt, der sowohl die Grundlagen als auch ihre Höhepunkte enthält. Die Darstellung führt den Leser in konkreter Weise in das... more...

#### Simple Extensions with the Minimum Degree Relations of Integral Domains

CRC Press 2007; US$ 231.00Although 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... more...

#### Syzygies and Hilbert Functions

CRC Press 2007; US$ 231.00Hilbert functions and resolutions are both central objects in commutative algebra and fruitful tools in the fields of algebraic geometry, combinatorics, commutative algebra, and computational algebra. Spurred by recent research in this area, Syzygies and Hilbert Functions explores fresh developments in the field as well as fundamental concepts. Written... more...

#### Determinantal Ideals

Birkhäuser Basel 2007; US$ 73.89This comprehensive overview of determinantal ideals includes an analysis of the latest results. Following the carefully structured presentation, you?ll develop new insights into addressing and solving open problems in liaison theory and Hilbert schemes. more...

#### Modules over Discrete Valuation Domains

De Gruyter 2008; US$ 200.54This book provides the first systematic treatment of modules over discrete valuation domains which plays an important role in various areas of algebra, especially in commutative algebra. Many important results representing the state of the art are presented in the text which is supplemented by exercises and interesting open problems. ... more...

#### Difference Algebra

Springer Netherlands 2008; US$ 91.84This book contains a systematic study of partial difference algebraic structures and their applications, as well as coverage of the classical theory of ordinary difference rings and field extensions. more...