Let G , H be non empty double loop structures and let I 1 be a map from G into H . If f is linear and g is linear, then g f is linear. In the sequel f is a ring morphisms structure. Let us consider f . Let G be a non empty double loop structure.
G is linear.
Let I 1 be a ring morphisms structure. I 1 is linear. Let us observe that there exists a ring morphisms structure which is strict and morphism of rings-like. A morphism of rings is a morphism of rings-like ring morphisms structure. Let us consider G .