= Fractional ideal
{title2=$I\subseteq Q(A)$}
{wiki}
For an <integral domain> $A$ with <fraction field> $K$, a fractional ideal is a nonzero $A$-submodule $I\subseteq K$ for which $dI\subseteq A$ for some $0\ne d\in A$. A finitely generated submodule of $K$ has a common denominator and is therefore a fractional ideal. The product is generated by pairwise products of elements. An <invertible fractional ideal> has a multiplicative inverse and is finitely generated; arbitrary fractional ideals need not be finitely generated over a non-Noetherian domain. The familiar fractional ideals of a <number field> are the special case $A=\mathcal O_K$. This general definition also applies to the ideals representing <Cartier divisors> on affine integral schemes.
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