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Produktbild: Difference Algebra
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Difference Algebra

Aus der Reihe Algebra and Applications
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93,99 € UVP 106,99 €

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

28.10.2010

Verlag

Springer Netherland

Seitenzahl

521

Maße (L/B/H)

23,5/15,5/2,9 cm

Gewicht

803 g

Auflage

Softcover reprint of hardcover 1st ed. 2008

Sprache

Englisch

ISBN

978-90-481-7774-5

Beschreibung

Rezension

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)

Zitat

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)

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

28.10.2010

Verlag

Springer Netherland

Seitenzahl

521

Maße (L/B/H)

23,5/15,5/2,9 cm

Gewicht

803 g

Auflage

Softcover reprint of hardcover 1st ed. 2008

Sprache

Englisch

ISBN

978-90-481-7774-5

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: ProductSafety@springernature.com

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  • Produktbild: Difference Algebra
  • Preface.
    1. Preliminaries. 1.1 Basic terminology and background material. 1.2 Elements of the theory of commutative rings. 1.3 Graded and filtered rings and modules. 1.4 Numerical polynomials. 1.5 Dimension polynomials of sets of m-tuples. 1.6 Basic facts of the field theory. 1.7 Derivations and modules of differentials. 1.8 Gröbner Bases.
    2. Basic concepts of difference algebra. 2.1 Difference and inversive difference rings. 2.2 Rings of difference and inversive difference polynomials. 2.3 Difference ideals. 2.4 Autoreduced sets of difference and inversive difference polynomails. Characteristic sets. 2.5 Ritt difference rings. 2.6 Varieties of difference polynomials.
    3. Difference modules. 3.1 Rings of difference operators. Difference modules. 3.2 Dimension polynomials of difference modules. 3.3 Gröbner Bases with respects to several orderings and multivariable dimension polynomials of difference modules. 3.4 Inversive difference modules. 3.5 s*-Dimension polynomials and their invariants. 3.6 Dimension of general difference modules.
    4. Difference field extensions. 4.1 Transformal dependence. Difference transcendental bases and difference transcendental degree. 4.2 Dimension polynomials of difference and inversive difference field extensions. 4.3 Limit degree. 4.4 The fundamental theorem on finitely generated difference field extensions. 4.5 Some results on ordinary difference field extensions. 4.6 Difference algebras.
    5. Compatibility, Replicability, and Monadicity. Difference specializations. 5.1 Compatible and incompatible difference field extensions. 5.2 Difference kernels over ordinary difference fields. 5.3 Difference specializations. 5.4 Babbitt's decomposition. Criterion of compatibility. 5.5 Replicability. 5.6 Monadicity.
    6. Difference kernels over partial difference fields. Difference valuation rings. 6.1 Difference kernels over partial difference fields and their prolongations. 6.2 Realizations of difference kernels over partial difference fields. 6.3 Difference valuation rings and extensions of difference specializations.
    7. Systems of algebraic difference equations. 7.1 Solutions of ordinary difference polynomials. 7.2 Existence theorem for ordinary algebraic difference equations. 7.3 Existence of solutions of difference polynomials in the case of two translations. 7.4 Singular and Multiple Realizations. 7.5 Review of further results on varieties of ordinary difference polynomials. 7.6 Ritt's number. Greenspan's and Jacobi's Bounds. 7.7 Dimension polynomials and the strength of a system of algebraic difference equations.
    8. Elements of the difference galois theory. 8.1 Galois correspondence for difference field extensions. 8.2 Picard-Vessiot theory of linear homogeneous difference equations. 8.3 Picard-Vessiot rings and galois theory of difference equations.
    Bibliography.
    Index.