Cring

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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.