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#### Noncommutative Iwasawa Main Conjectures over Totally Real Fields

Springer Berlin Heidelberg 2012; US$ 139.00The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives. Non-commutative Iwasawa theory has emerged dramatically over the last decade, culminating in the recent proof of the non-commutative... more...

#### Module Theory

Springer 2012; US$ 39.95The purpose of this expository monograph is three-fold. First, the solution of a problem posed by Wolfgang Krull in 1932 is presented. He asked whether what is now called the 'Krull-Schmidt Theorem' holds for artinian modules. A negative answer was published only in 1995 by Facchini, Herbera, Levy and Vámos. Second, the answer to a question... more...

#### How To Pass Flash Revise Higher Maths

Hodder Education 2011; US$ 41.58A handy pocketbook, full of quick-fire questions on the key facts for each topic in Higher Maths - ideal for instant revision. more...

#### Dynamics, Statistics and Projective Geometry of Galois Fields

Cambridge University Press 2010; US$ 32.00V. I. Arnold reveals some unexpected connections between Galois fields and other apparently unrelated theories. more...

#### Serre's Problem on Projective Modules

Springer Berlin Heidelberg 2010; US$ 119.00?Serre?s Conjecture?, for the most part of the second half of the 20th century, - ferred to the famous statement made by J. -P. Serre in 1955, to the effect that one did not know if ?nitely generated projective modules were free over a polynomial ring k[x ,. . . ,x], where k is a ?eld. This statement was motivated by the fact that 1 n the af?ne scheme... 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...

#### Higher-Dimensional Geometry over Finite Fields

IOS Press 2008; US$ 161.00Number systems based on a finite collection of symbols, such as the 0s and 1s of computer circuitry, are ubiquitous in the modern age. Finite fields are the important number systems. This title introduces the reader to the developments in algebraic geometry over finite fields. 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...

#### Ideals and Reality

Springer Berlin Heidelberg 2006; US$ 119.00Besides giving an introduction to Commutative Algebra - the theory of c- mutative rings - this book is devoted to the study of projective modules and the minimal number of generators of modules and ideals. The notion of a module over a ring R is a generalization of that of a vector space over a field k. The axioms are identical. But whereas every vector... more...