Chapter II(*)

Localization

The conventions of Chapter I remain in force in this chapter. Also, unless otherwise stated, all rings are assumed to be commutative.

Let $A, B$ be two rings, $\varphi$ a homomorphism from $A$ to $B$ and $M$ a $B$-module. When we speak of $M$ as an $A$-module, we mean, unless otherwise stated, with the $A$-module structure $\varphi_*(M)$ (defined by the external law $(a, m) \mapsto \varphi(a)m$).