Algebraic Differential Calculus

Title: Algebraic Differential Calculus
Contents
Chapter I. Kaehler Differentials
1_1 Derivations Tangent Spaces and Vector Fields
1_2 The Module of Kaehler Differentials Tangent Bundles
1_3 Differential Modules of Field Extensions
1_4 Differential Modules of Local Rings
1_5 Differential Modules of Affine Algebras and their Localizations
1_6 Smooth Algebras
1_7 Differential Modules of Complete Intersections
1_8 Existence of Universally Finite Derivations
1_9 The Kaehler Differents (Jacobian Ideals) of an Algebra
Introduction to the bibliography I
Chapter I I. Differential Operators
2_1 Basic Properties of Differential Operators
2_2 Universal Differential Operators
2_3 Functorial Properties
2_4 Differential Operators of Smooth Algebras
Introduction to the bibliography I I
Chapter I I I. Differential Forms
3_1 Differential Algebras
3_2 The Universal Differential Algebra. Universal Extension of Differential Algebras
3_3 Functorial Properties of the Universal Extension
Introduction to the bibliography I I I
Chapter IV. Connections
4_1 Connections on Modules
4_2 Curvature and Torsion of Connections
4_3 Riemannian Algebras
4_4 The Levi-Civita Connection
4_5 Curvature of Riemannian Algebras
Solutions to some of the problems
Appendices
A Commutative Algebras
B Dimension Formulas in Algebras of Finite Type. Quasifinite and Equidimensional Algebras
C Complete Intersections
D The Fitting Ideals of a Module
Bibliography