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Ideals and Realityby Friedrich Ischebeck; Ravi A. Rao
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG 2005; US$ 105.00This monograph tells the story of a philosophy of J-P. Serre and his vision of relating that philosophy to problems in affine algebraic geometry. It gives a lucid presentation of the Quillen-Suslin theorem settling Serre's conjecture. The central topic of the book is the question of whether a curve in $n$-space is as a set an intersection of $(n-1)$ hypersurfaces, depicted by the central theorems of Ferrand, Szpiro, Cowsik-Nori, Mohan Kumar, Boratynsk. The book gives a comprehensive introduction to basic commutative algebra, together with the related methods from homological algebra, which will enable students who know only the fundamentals of algebra to enjoy the power of using these tools. At the same time, it also serves as a valuable... more...
Higher-Dimensional Geometry over Finite Fieldsby D. Kaledin; Y. Tschinkel
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...
Modules over Discrete Valuation Domainsby Piotr A. Krylov; Askar A. Tuganbaev
Walter de Gruyter, Inc. 2008; US$ 188.00This 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. An important contribution to commutative algebra. more...
Serre's Problem on Projective Modulesby T.Y. Lam
Springer 2005; US$ 119.00Presents some of the most comprehensive view available on the mathematics of 'Serre's Conjecture'. This title includes such coverage as stably free modules and the basic calculus of unimodular rows, Suslin's Normality and Factorial Theorems, and a survey of research since 1978. more...
Dynamics, Statistics and Projective Geometry of Galois Fieldsby V. I. Arnold
Cambridge University Press 2010; US$ 22.00V. I. Arnold reveals some unexpected connections between Galois fields and other apparently unrelated theories. more...
Polynomials and Equationsby K.T. Leung; S.N. Suen; Ida A.C. Mok
Hong Kong University Press 1992; US$ 21.00Primarily a textbook to prepare Sixth Form students for public examinations in Hong Kong, this book is also useful as a reference for undergraduate students since it contains some advanced theory of equations beyond the sixth form level. more...
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