---

＜電子ブック＞
Difference Algebra / by Alexander Levin
(Algebra and Applications. ISSN:21922950 ; 8)

版	1st ed. 2008.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2008
本文言語	英語
大きさ	XI, 521 p : online resource
著者標目	*Levin, Alexander author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Algebraic fields LCSH:Polynomials LCSH:Commutative algebra LCSH:Commutative rings LCSH:Difference equations LCSH:Functional equations FREE:Algebra FREE:Field Theory and Polynomials FREE:Commutative Rings and Algebras FREE:Difference and Functional Equations
一般注記	Preliminaries -- Basic Concepts of Difference Algebra -- Difference Modules -- Difference Field Extensions -- Compatibility, Replicability, and Monadicity -- Difference Kernels over Partial Difference Fields. Difference Valuation Rings -- Systems of Algebraic Difference Equations -- Elements of the Difference Galois Theory 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 HTTP:URL=https://doi.org/10.1007/978-1-4020-6947-5

 類似資料