## Ring

### Set

 context $\langle X,+ \rangle \in \mathrm{AbelianGroup}(X)$ definiendum $\langle X,+,* \rangle\in\mathrm{it}$ for all $a,b,c\in X$ postulate $(a*b)*c=a*(b*c)$ postulate $a*(b+c)=(a*b)+(a*c)$ postulate $(b+c)*a=(b*a)+(c*a)$

### Discussion

One might call the commutative group operation “$+$” the addition and the other one “$*$” the multiplication. In a unital ring, the latter has an identity too.

One generally calls $X$ the ring, i.e. the set where the operations “$+$” and “$*$” are defined on.

Wikipedia: Ring