§ 1. Derivations.- § 2. Differential Algebras.- § 3. Universal Extension of a Differential Algebra.- § 4. Description of the Universal Extension in Special Cases.- § 5. Differential Modules of Field Extensions.- § 6. Differential Modules of Local Rings.- § 7. Differential Modules of Affine Algebras.- § 8. Smooth Algebras.- § 9. Differential Modules of Complete Intersections.- § 10. The Kahler Differents (Jacobian Ideals) of an Algebra.- § 11. Universally Finite Differential Algebras.- § 12. Differential Algebras and Completion.- § 13. Differential Modules of Semianalytic Algebras.- § 14. Regularity Criteria for Semianalytic Algebras.- § 15. Existence of p-Bases.- § 16. Traces of Differential Forms.- § 17. Residues in Algebraic Function Fields of one Variable.- Appendices.- A. Commutative Algebras.- B. Dimension Formulas in Algebras of Finite Type.- C. Complete Intersections.- D. The Fitting Ideals of a Module.- E. The Dual of a Module over a Noetherian Ring.- F. Traces.- G. Differents.- Symbol Index.
Inhaltsverzeichnis
§ 1. Derivations. - § 2. Differential Algebras. - § 3. Universal Extension of a Differential Algebra. - § 4. Description of the Universal Extension in Special Cases. - § 5. Differential Modules of Field Extensions. - § 6. Differential Modules of Local Rings. - § 7. Differential Modules of Affine Algebras. - § 8. Smooth Algebras. - § 9. Differential Modules of Complete Intersections. - § 10. The Kahler Differents (Jacobian Ideals) of an Algebra. - § 11. Universally Finite Differential Algebras. - § 12. Differential Algebras and Completion. - § 13. Differential Modules of Semianalytic Algebras. - § 14. Regularity Criteria for Semianalytic Algebras. - § 15. Existence of p-Bases. - § 16. Traces of Differential Forms. - § 17. Residues in Algebraic Function Fields of one Variable. - Appendices. - A. Commutative Algebras. - B. Dimension Formulas in Algebras of Finite Type. - C. Complete Intersections. - D. The Fitting Ideals of a Module. - E. The Dual of a Module over a Noetherian Ring. - F. Traces. - G. Differents. - Symbol Index.
