Cring

Definition
A cring is a set equipped with the following structures:


 * 1) An abelian group structure with binary operation denoted by $$+$$ and identity element denoted by $$0$$.
 * 2) A binary operation $$*$$ that is a 2-cocycle for trivial group action of the abelian group on itself, such that $$x * 0 = 0 * x = 0$$ for all $$x$$ in the set.