Congruence modulo an ideal
= Congruence modulo an ideal
{title2=$a\equiv b\pmod I\iff a-b\in I$}
= Ring congruence
{synonym}
Two elements of a <commutative ring> are congruent modulo an <ideal> if their difference lies in that <ideal>, equivalently if their images in the <quotient ring> agree. This is an <equivalence relation> compatible with <addition> and <multiplication>. For $R=\mathbb Z_p[[T]]$ and $I=p^kR$, it means every coefficient difference is divisible by $p^k$.