Let R be an associative ring with identity and let Q be the field of rational numbers. Then \(R^ Q=R\otimes Q\) is a finite dimensional Q- algebra with identity. The author gives the definition: The ring R is called rigid if the group of automorphisms of R is formed only by the identity map. The author proves that: If R is a rigid ring, then the algebra \(R^ Q\) is a direct sum of algebras, which are either commutative or division rings of generalized quaternions.