Picard group of a ring
= Picard group of a ring
{c}
{title2=$\operatorname{Pic}(A)$}
The <Picard group> of a commutative <ring> $A$ consists of isomorphism classes of finitely generated <projective modules> that have rank one at every <prime ideal>. Tensor product is the group law, $[A]$ is the identity, and the module dual supplies the inverse. For an <integral domain>, every such module can be represented by an <invertible fractional ideal> after choosing a basis over the <fraction field>.