Let 
be a number
field with ring of integers 
and let 
be a nontrivial ideal of 
. Then the ideal class of 
, denoted ![[A]](/https/mathworld.wolfram.com/images/equations/IdealClass/Inline6.svg)
, is the set of fractional
ideals 
such that there exists a nonzero element 
of 
such that 
.
Ideal Class
See also
Class Group, Ideal, Minkowski's Lemma, Number Field, Number RingThis entry contributed by David Terr
Explore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W., with contributions by David Terr. "Ideal Class." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IdealClass.html