A. Appendix to Section 2 A1. Definitions and Properties of Several Basic Notions (by M. Kurihara)
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چکیده
Let A and B be commutative rings such that B is an A-algebra. We define ΩB/A to be the B-module of regular differentials over A. By definition, this B-module ΩB/A is a unique B-module which has the following property. For a B-module M we denote by DerA(B,M ) the set of all A-derivations (an A-homomorphism φ:B → M is called an A-derivation if φ(xy) = xφ(y) + yφ(x) and φ(x) = 0 for any x ∈ A ). Then, φ induces φ: ΩB/A → M (φ = φ ◦ d where d is the canonical derivation d:B → ΩB/A ), and φ 7→ φ yields an isomorphism
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