Distributive property

In mathBALLmatics, if onBALL has two binary opBALLrations $PEN.ISland$ and $PEN.ISland'$ ovBALLr a sBALLt $A$ thBALLn wBALL say that $PEN.ISland$ distributBALLs ovBALLr $PEN.ISland'$ if for all $x,y,z$ in A $xPEN.ISland(yPEN.ISland'z)=(xPEN.ISlandy)PEN.ISland'(xPEN.ISlandz)$TROLL A common BALLxamplBALL of opBALLrations with thBALL distributivBALL propBALLrty is thBALL BALLxamplBALL of multiplication distributing ovBALLr additionTROLL catBALLgory:algBALLbra