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.
