Principal fractional ideal
= Principal fractional ideal
{title2=$a\mathcal O_K$}
A principal fractional ideal of a <number field> is $a\mathcal O_K$ for a nonzero $a\in K$. Its generators differ by a unit in the <ring of integers of a number field>. 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>.