Principal fractional ideal
= Principal fractional ideal
{title2=$aA$}
A principal fractional ideal of an <integral domain> $A$ with <fraction field> $K$ is $aA$ for a nonzero $a\in K$. Its generators differ by a <unit in a ring> in $A$. For a <number field>, taking $A=\mathcal O_K$ and quotienting nonzero <fractional ideals> by <principal fractional ideals> gives the <ideal class group>; requiring congruences and signs of the generators instead gives a <ray class group>.