===== Semiring =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $X$ |

| @#FFBB00: definiendum | @#FFBB00: $\langle X,+,* \rangle \in \mathrm{Semiring}(X)$ |

| @#55CCEE: context     | @#55CCEE: $\langle X,+ \rangle \in \mathrm{AbelianMonoid}(X)$ |
| $a,b,c\in X$ |

| @#55EE55: postulate   | @#55EE55: $(a*b)*c=a*(b*c)$ |
| @#55EE55: postulate   | @#55EE55: $a*(b+c)=(a*b)+(a*c)$ |
| @#55EE55: postulate   | @#55EE55: $(b+c)*a=(b*a)+(c*a)$ |

==== Discussion ====
=== Reference ===
Wikipedia: [[https://en.wikipedia.org/wiki/Semiring|Semiring]]
==== Parents ====
=== Context ===
[[Abelian monoid]]