Interpolation ordered algebraic systems

Partially ordered algebraic systems such as linear spaces over partially ordered skew fields, pseudo-ordered rings and algebras over partially ordered fields are considered. This order of a ring (an algebra) is similar to a partial order of a Lie algebra, which was introduced by Kopytov. Those orders are induced onto nonassociative rings (algebras) (Lie rings, Jordan rings, for example) by partial orders of their additive groups. Second and third theorems of order isomorphisms for interpolation ordered systems are proved.