distributivity

Given a set (http://planetmath.org/Set) $S$ with two binary operations $+:S\times S\to S$ and $\cdot :S\times S\to S$, we say that $\cdot$ is right distributive over $+$ if

$$(a+b)\cdot c=(a\cdot c)+(b\cdot c)\mathrm{for}\mathrm{all}a,b,c\in S$$

and left distributive over $+$ if

$$a\cdot (b+c)=(a\cdot b)+(a\cdot c)\mathrm{for}\mathrm{all}a,b,c\in S.$$

If $\cdot$ is both left and right distributive over $+$, then it is said to be distributive over $+$ (or, alternatively, we may say that $\cdot$ distributes over $+$).

Title	distributivity
Canonical name	Distributivity
Date of creation	2013-03-22 13:47:00
Last modified on	2013-03-22 13:47:00
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	15
Author	yark (2760)
Entry type	Definition
Classification	msc 06D99
Classification	msc 16-00
Classification	msc 13-00
Classification	msc 17-00
Synonym	distributive law
Synonym	distributive property
Related topic	Ring
Related topic	DistributiveLattice
Related topic	NearRing
Defines	distributive
Defines	left distributive
Defines	right distributive
Defines	left-distributive
Defines	right-distributive
Defines	distributes over
Defines	left distributivity
Defines	right distributivity
Defines	left distributes over
Defines	left distributive law
Defines	right distributive law