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| File | Description | Size | Format | |
|---|---|---|---|---|
| Lectures_in_Mathematics_16.pdf | 18.28 MB | Adobe PDF | View/Open |
| Title: | Differential algebra of nonzero characteristic |
| Authors: | Okugawa, Kôtaro |
| Author's alias: | 奥川, 光太郎 |
| Keywords: | Algebra Differential |
| Issue Date: | 1987 |
| Publisher: | Kinokuniya |
| Journal title: | Lectures in Mathematics |
| Volume: | 16 |
| Table of contents: | Foreword [ix] Chapter 1 Derivations 1.1 Conventions [1] 1.2 Definitions and elementary properties [2] 1.3 Examples of derivations [7] 1.4 Derivatives of powers [12] 1.5 Taylor expansion [13] 1.6 Rings of quotients [15] 1.7 Separably algebraic extension fields [20] 1.8 Inseparably algebraic extension fields [24] Chapter 2 Differential Rings and Differential Fields 2.1 Definitions [31] 2.2 Differential ring of quotients [35] 2.3 Differential polynomials [37] 2.4 Differential ideals [44] 2.5 Differential homomorphisms and differential isomorphisms [48] 2.6 Contractions and extensions of differential ideals [49] 2.7 Separably algebraic extension fields of a differential field [54] 2.8 Inseparably algebraic extension fields of a differential field [55] 2.9 The field of constants of a differential field [58] Chapter 3 Differential Ideals 3.1 Perfect and prime differential ideals [61] 3.2 Conditions of Noether [65] 3.3 Differential rings satisfying the condition of Noether for ideals [67] 3.4 Differential polynomial rings [70] 3.5 Linear differential polynomials [74] 3.6 Linear dependence over constants [77] 3.7 Results about constants [82] 3.8 Extension of the differential field of coefficients [85] Chapter 4 Universal Differential Extension Field 4.1 Definitions [95] 4.2 Lemmas [96] 4.3 The existence theorem [99] 4.4 Some properties of the universal differential extension field [100] 4.5 Linear homogeneous differential polynomial ideals [101] 4.6 Primitive elements [102] 4.7 Exponential elements [104] 4.8 Weierstrassian elements [107] Chapter 5 Strongly Normal Extensions 5.1 Some properties of differential closure [112] 5.2 Conventions [116] 5.3 Differential isomorphisms [116] 5.4 Specializations of differential isomorphisms [119] 5.5 Strong differential isomorphisms [125] 5.6 Strongly normal extensions and Galois groups [133] 5.7 The fundamental theorems [141] 5.8 Examples [152] 5.9 Differential Galois cohomology [154] Chapter 6 Picard-Vessiot Extensions 6.1 Picard-Vessiot extension whose Galois group is the general linear group [160] 6.2 Fundamental theorems of Galois theory for Picard-Vessiot extensions [163] 6.3 Picard-Vessiot extension by a primitive [168] 6.4 Picard-Vessiot extension by an exponential [171] 6.5 Liouvillian extensions [173] Bibliography [185] Index of Notations [187] Index of Terminologies [189] |
| URI: | http://hdl.handle.net/2433/84921 |
| Appears in Collections: | Lectures in Mathematics : Department of Mathematics, Kyoto University |
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