The Stacks project

Definition 111.22.3. Let $A$ be a ring. The class group of $A$, sometimes called the Picard group of $A$ is the set $\mathop{\mathrm{Pic}}\nolimits (A)$ of isomorphism classes of invertible $A$-modules endowed with a group operation defined by tensor product (see Exercise 111.22.2).

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