UID:
almahu_9949697348202882
Format:
1 online resource (469 p.)
ISBN:
1-281-76653-4
,
9786611766535
,
0-08-087369-3
Series Statement:
Pure and applied mathematics; a series of monographs and textbooks ; v. 54
Content:
Differential Algebra & Algebraic Groups
Note:
Description based upon print version of record.
,
Front Cover; Differential Algebra and Algebraic Groups; Copyright Page; Contents; Preface; Acknowledgments; Chapter 0. Algebraic Preliminaries; 1. Conventions; 2. Separable dependence; 3. Quasi-separable field extensions; 4. Quotients; 5. Perfect ideals; 6. Separable, quasi-separable, and regular ideals; 7. Conservative systems; 8. Perfect conservative systems; 9. Noetherian conservative systems; 10. Morphisms and birational equivalence of ideals; 11. Polynomial ideals and generic zeros; 12. Polynomial ideals and ground field extension; 13. Power series; 14. Specializations
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15. Algebraic function fields of one variable16. Dimension of components; 17. Lattice points; 18. Shapiro's lemma; 19. t-Values; Chapter I. Basic Notions of Differential Algebra; 1. Differential rings; 2. Homomorphisms and differential ideals; 3. Differential rings of quotients; 4. Transformation and restriction of the set of derivation operators; 5. Differential modules; differential algebras; 6. Differential polynomial algebras; 7. Permissible gradings; 8. Rank; 9. Autoreduced sets; 10. Characteristic sets; 11. Pseudo-leaders; 12. Differential algebras of power series
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Chapter II. Differential Fields1. Linear dependence over constants; 2. Separable extensions; 3. Differentially perfect and differentially quasi-perfect differential fields; 4. Separable dependence over constants; 5. Differential polynomial functions; 6. Dependence of derivative operators; 7. Differentially separable dependence; 8. Differentially separable extensions; 9. Differential inseparability bases; 10. Differential transcendence bases; 11. Finitely generated extensions; 12. Differential inseparability polynomials; 13. Differential type; typical differential inseparability degree
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Chapter III. The Basis Theorem and Some Related Topics1. Differential conservative systems; 2. Quasi-separable differential ideals; 3. Differential fields of definition; 4. The basis theorem; 5. Differential dimension polynomials; 6. Extension of the differential field of coefficients; 7. Universal extensions; 8. t-Coherent autoreduced sets; 9. Differential specializations; 10. Constrained families; Chapter IV. Algebraic Differential Equations; PART A: CHARACTERISTIC p ARBITRARY; 1. Differential affine space. The differential Zariski topology; 2. Generic zeros. The theorem of zeros
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3. Closed sets and u-separable differential ideals4. The relative topologies; differential fields of definition; 5. Linear differential ideals; 6. General components; 7. General components and differential dimension polynomials; 8. Multiplicity of zeros; PART B: CHARACTERISTIC p = 0; 9. Finite sets of differential polynomials; 10. The leading coefficient theorem; 11. Levi's lemma; 12. The domination lemma; 13. Preparations; 14. The component theorem; 15. The low power theorem; 16. The Ritt problem; 17. Systems of bounded order; 18. Substitution of powers; Bibliography for Chapters I-IV
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Chapter V. Algebraic Groups
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English
Additional Edition:
ISBN 0-12-417650-X
Language:
English
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