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Algebra and Applications

Difference Algebra

Authors: Levin, Alexander

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  • 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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eBook 83,29 €
price for Spain (gross)
  • ISBN 978-1-4020-6947-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-1-4020-6946-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 103,99 €
price for Spain (gross)
  • ISBN 978-90-481-7774-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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 self-contained; 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)

Table of contents (8 chapters)

Buy this book

eBook 83,29 €
price for Spain (gross)
  • ISBN 978-1-4020-6947-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-1-4020-6946-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 103,99 €
price for Spain (gross)
  • ISBN 978-90-481-7774-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Difference Algebra
Authors
Series Title
Algebra and Applications
Series Volume
8
Copyright
2008
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-6947-5
DOI
10.1007/978-1-4020-6947-5
Hardcover ISBN
978-1-4020-6946-8
Softcover ISBN
978-90-481-7774-5
Series ISSN
1572-5553
Edition Number
1
Number of Pages
XI, 521
Topics