= Base change of invertible modules
{title2=$L\mapsto B\otimes_A L$}
For a <ring homomorphism> $A\to B$, <extension of scalars> takes an <invertible module> to an invertible $B$-module. A direct-summand presentation in a finite <free module> remains a direct-summand presentation after tensoring. At a prime $\mathfrak q\subset B$ contracting to $\mathfrak p$, localization gives $B_{\mathfrak q}\otimes_{A_{\mathfrak p}}L_{\mathfrak p}\cong B_{\mathfrak q}$. Compatibility with tensor products, identities and composition makes the <Picard group of a ring> a covariant <functor>.
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