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Catalogue Information
Field name	Details
Dewey Class	512.3
Title	Difference Algebra ([Ebook]) / by Alexander Levin.
Author	Levin, Alexander
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : Springer Netherlands , 2008.
Physical Details	XI, 521 pages : online resource.
Series	Algebra and Applications ; 8
ISBN	9781402069475
Summary Note	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 self-contained; it requires no prerequisites other than knowledge of basic algebraic concepts and mathematical maturity of an advanced undergraduate.:
Contents note	Preface -- 1. Preliminaries -- 2. Basic concepts of difference algebra -- 3. Difference modules -- 4. Difference field extensions -- 5. Compatibility, Replicability, and Monadicity. Difference specializations -- 6. Difference kernels over partial difference fields -- Difference valuation rings -- 7. Systems of algebraic difference equations -- 8. Elements of the difference galois theory -- Bibliography -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4020-6947-5
Links to Related Works	Subject References: Algebra . Commutative Rings and Algebras . Difference and Functional Equations . Field Theory and Polynomials . Field theory (Physics) . Functional equations . Mathematics . Authors: Levin, Alexander . Corporate Authors: SpringerLink (Online service) . Series: Algebra and Applications . Classification: 512.3 . 512.32 (DDC 23) .

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Difference Algebra

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