Rig

A rig is a generalized ring which may lack negatives. That is, a rig $(𝑅, +, \cdot)$ consists of a Commutative monoid $(𝑅, +)$ called addition and a Monoid $(𝑅, \cdot)$ called multiplication, with the extra conditions #m/def/ring

left-distributivity $𝑎 \cdot (𝑏 + 𝑐) = (𝑎 \cdot 𝑏) + 𝑎 \cdot 𝑐)$
right-distributivity $(𝑏 + 𝑐) \cdot 𝑎 = (𝑏 \cdot 𝑎) + (𝑐 \cdot 𝑎)$
left-annihilation $0 \cdot 𝑎 = 0$
right-annihilation $𝑎 \cdot 0 = 0$

where $0$ is the additive identity.

#state/develop | #lang/en | #SemBr