 First monograph on difference algebra that covers partial algebraic structures, and the only monograph on the subject published in the last forty years
 Contains new ideas and technique (such as construction of Gröbner bases with respect to several orderings and the concepts of multivariable dimension polynomials) that can be efficiently applied in various areas of algebra and algebraic geometry
 Contains an important application of the algebraic technique to the study of the A. Einstein's concept of strength of systems of difference equations of mathematical physics
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 About this book

Difference algebra grew out of the study of algebraic difference equations with coefficients from functional fields in much the same way as the classical algebraic geometry arose from the study of polynomial equations with numerical coefficients. The first stage of the 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, difference algebra has overgrew the frame of the theory of ordinary algebraic difference equations and appears as a rich theory with applications to the study of equations in finite differences, functional equations, differential equations with delay, algebraic structures with operators, group and semigroup rings.
This book reflects the contemporary level of difference algebra; it contains a systematic study of partial difference algebraic structures and their applications, as well as the coverage of the classical theory of ordinary difference rings and field extensions. The monograph is intended for graduate students and researchers in difference and differential algebra, commutative algebra, ring theory, and algebraic geometry. It will be also of interest to researchers in computer algebra, theory of difference equations and equations of mathematical physics. The book is selfcontained; it requires no prerequisites other than knowledge of basic algebraic concepts and mathematical maturity of an advanced undergraduate.
 Reviews

From the reviews:
“Levin’s Difference Algebra [40] is a milestone in the subject. It is an ever so fundamental and detailed work, in which one does not require the ordinary case of one selected automorphism…an excellent source of numerous results and techniques” (Bulletin of the London Mathematical Society, April 16, 2011)
“This book gives a systematic study of both ordinary and partial difference algebraic structures and their applications. … The book will long become a good reference for researchers in the area of difference algebra and algebraic structures with operators.” (Hirokazu Nishimura, Zentralblatt MATH, Vol. 1209, 2011)
 Table of contents (8 chapters)


Preliminaries
Pages 1102

Basic Concepts of Difference Algebra
Pages 103154

Difference Modules
Pages 155244

Difference Field Extensions
Pages 245309

Compatibility, Replicability, and Monadicity
Pages 311370

Table of contents (8 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Difference Algebra
 Authors

 Alexander Levin
 Series Title
 Algebra and Applications
 Series Volume
 8
 Copyright
 2008
 Publisher
 Springer Netherlands
 Copyright Holder
 Springer Science+Business Media B.V.
 eBook ISBN
 9781402069475
 DOI
 10.1007/9781402069475
 Hardcover ISBN
 9781402069468
 Softcover ISBN
 9789048177745
 Series ISSN
 15725553
 Edition Number
 1
 Number of Pages
 XI, 521
 Topics