rig

A rig $(R,+,\cdot )$ is a set $R$ together with two binary operations $+:R^2\to R:(a,b)\mapsto a+b$ and $\cdot :R^2\to R:(a,b)\mapsto ab$, such that both $(R,+)$ and $(R,\cdot )$ are monoids, where $\cdot$ distributes over $+$. That is if $\{a,b,c,d\}\subset R$ then $(a+b)(c+d)=ac+ad+bc+bd$. The natural numbers with ordinary addition and multiplication $(𝐍,+,\cdot )$ is a rig.

A rig $(R,+,\cdot )$ is a ring if $(R,+)$ is a group. The integers with ordinary addition and multiplication $(𝐙,+,\cdot )$ is a ring.

Title	rig
Canonical name	Rig
Date of creation	2013-03-22 14:44:29
Last modified on	2013-03-22 14:44:29
Owner	HkBst (6197)
Last modified by	HkBst (6197)
Numerical id	8
Author	HkBst (6197)
Entry type	Definition
Classification	msc 20M99
Related topic	semigroup
Related topic	ring