# distributive

If + and $$\cdot$$ are binary operations on a given set, then we say that $$\cdot$$ is left-distributive over + if for any elements $$a$$, $$b$$, and $$c$$ in the set we have $$a\cdot (b+c)=a\cdot b+a\cdot c$$. Similarly we say that $$\cdot$$ is right-distributive over + if for any elements $$a$$, $$b$$, and $$c$$ in the set we have $$(b+c)\cdot a=b\cdot a+c\cdot a$$. If $$\cdot$$ is both left and right distributive over + then we say simply that it is distributive over +.

The fact that in arithmetic multiplication is distributive over addition is referred to as the distributive property of arithmetic.