An D21: Algebraic structure $R = (X, +, \times)$ is a ringoid if and only if

(1)	$\forall \, x, y \in X : x + y \in X$ (D20: Enclosed binary operation)
(2)	$\forall \, x, y \in X : x y \in X$ (D20: Enclosed binary operation)
(3)	$\forall \, x, y, z \in X : x (y + z) = (x y) + (x z)$ (D555: Left-distributive binary operation)
(4)	$\forall \, x, y, z \in X : (x + y) z = (x z) + (y z)$ (D556: Right-distributive binary operation)