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#### Cyclotomic Fields and Zeta Values

Springer Berlin Heidelberg 2006; US$ 64.95Cyclotomic 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...

#### Number Fields and Function Fields

Springer 2006; US$ 104.00Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas. This title contains articles which explore various aspects of the parallel worlds of function fields and number fields, ranging from Arakelov geometry to Drinfeld modules, and t-motives. more...

#### Algebraische Zahlentheorie (Springer-Lehrbuch Masterclass) (German Edition)

Springer 2006; US$ 59.95Algebraische Zahlentheorie: eine der traditionsreichsten und aktuellsten Grunddisziplinen der Mathematik. Das vorliegende Buch schildert ausführlich Grundlagen und Höhepunkte. Konkret, modern und in vielen Teilen neu. Neu: Theorie der Ordnungen. Plus: die geometrische Neubegründung der Theorie der algebraischen Zahlkörper durch die "Riemann-Roch-Theorie"... more...

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

CRC Press 2007; US$ 231.00The Ring R[a] n R[a-1] Anti-Integral Extension and Flat Simple Extensions The Ring R(Ia) and the Anti-Integrality of a Strictly Closedness and Integral Extensions Upper-Prime, Upper-Primary, or Upper-Quasi-Primary Ideals Some Subsets of Spec(R) in the Birational Case SIMPLE EXTENSIONS OF HIGH DEGREE Sharma Polynomials Anti-Integral Elements... more...

#### Syzygies and Hilbert Functions

CRC Press 2007; US$ 231.00Some Results and Questions on Castelnuovo-Mumford Regularity Marc Chardin Hilbert Coefficients of Ideals with a View toward Blowup Algebras Alberto Corso and Claudia Polini A Case Study in Bigraded Commutative Algebra David Cox, Alicia Dickenstein and Hal Schenck Lex-Plus-Powers Ideals Christopher A. Francisco and Benjamin P. Richert Multiplicity... more...

#### Arithmetic of Finite Fields

Springer 2007; US$ 89.95This book constitutes the refereed proceedings of the First International Workshop on the Arithmetic of Finite Fields, WAIFI 2007, held in Madrid, Spain in June 2007. The 27 revised full papers presented were carefully reviewed and selected from 94 submissions. The papers are organized in topical sections on structures in finite fields, efficient implementation... more...

#### Modules over Discrete Valuation Domains

De Gruyter 2008; US$ 252.00This 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...

#### Modules and Comodules

Springer 2008; US$ 169.00The 23 articles in this volume encompass the proceedings of the International Conference on Modules and Comodules held in Porto (Portugal) in 2006 and dedicated to Robert Wisbauer on the occasion of his 65th birthday. These articles reflect Professor Wisbauer's wide interests and give an overview of different fields related to module theory, some... more...

#### Field Arithmetic

Springer 2008; US$ 219.00Explores Diophantine fields through their absolute Galois groups. This work features the techniques from algebraic geometry, number theory, and profinite groups. It helps graduate students to learn the generalizations of finite field ideas. more...

#### Difference Algebra

Springer 2008; US$ 139.00Difference algebra grew out of the study of algebraic difference equations with coefficients from functional fields. The first stage of this development of the theory is associated with its founder, J.F. Ritt (1893-1951), and R. Cohn, whose book Difference Algebra (1965) remained the only fundamental monograph on the subject for many years. Nowadays,... more...