Authors:
- 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
Part of the book series: Algebra and Applications (AA, volume 8)
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (8 chapters)
-
Front Matter
-
Back Matter
About this book
Difference 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, difference algebra has overgrown 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.
The monograph is intended for graduate students and researchers in difference and differential algebra, commutative algebra, ring theory, and algebraic geometry. The book is self-contained; it requires no prerequisites other than the knowledge of basic algebraic concepts and a 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)
Authors and Affiliations
-
The Catholic University of America, Washington, D.C., USA
Alexander Levin
Bibliographic Information
Book Title: Difference Algebra
Authors: Alexander Levin
Series Title: Algebra and Applications
DOI: https://doi.org/10.1007/978-1-4020-6947-5
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media B.V. 2008
Hardcover ISBN: 978-1-4020-6946-8Published: 16 April 2008
Softcover ISBN: 978-90-481-7774-5Published: 28 October 2010
eBook ISBN: 978-1-4020-6947-5Published: 19 April 2008
Series ISSN: 1572-5553
Series E-ISSN: 2192-2950
Edition Number: 1
Number of Pages: XI, 521
Topics: Algebra, Field Theory and Polynomials, Commutative Rings and Algebras, Difference and Functional Equations