[[Ring theory MOC]]
# 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
1. **left-distributivity** $a \cdot (b + c) = (a \cdot b) + a \cdot c)$
2. **right-distributivity** $(b + c) \cdot a = (b \cdot a) + (c \cdot a)$
3. **left-annihilation** $0 \cdot a = 0$
4. **right-annihilation** $a \cdot 0 = 0$

where $0$ is the additive identity.

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