We say that the binary operation "\(\cdot\)" is distributive over the binary operation "\( + \)", if the distributivity law \[(x+y)\cdot z=x\cdot z + y\cdot z\quad\quad\text{"right-distributivity property"}\] and \[x\cdot (y+z)=x\cdot y + x\cdot z\quad\quad\text{"left-distributivity property"}\] holds for any three elements \(x,y,z\) of an algebraic structure, in which these two operations are defined and for which the law is postulated.
Chapters: 1 2
Definitions: 3 4 5
Lemmas: 6
Proofs: 7 8 9 10 11 12
Propositions: 13
