# distributivity

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

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

and left distributive over $+$ if

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

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