| context | $X$ |
| definiendum | $\langle X,+,* \rangle \in \mathrm{Semiring}(X)$ |
| context | $\langle X,+ \rangle \in \mathrm{AbelianMonoid}(X)$ |
| $a,b,c\in X$ |
| postulate | $(a*b)*c=a*(b*c)$ |
| postulate | $a*(b+c)=(a*b)+(a*c)$ |
| postulate | $(b+c)*a=(b*a)+(c*a)$ |
Wikipedia: Semiring