R. H. Oehmke and R. Sandler have shown in [4] that the middle nucleus of a finite-dimensional semisimple Jordan algebra coincides with its center providing the base field has a characteristic different from 2. By the middle nucleus of a commutative algebra A we mean the set of those elements x in A, for which the associator (y, x, z) = (yx)z-y(xz) vanishes identically in y, zEA. Moreover, using this theorem and relying on methods from projective geometry, the authors proved that any two isotopic Jordan division algebras of finite dimension are isomorphic if the characteristic of the base field is also different from 3. The underlying concept of isotopy in this statement is due to A. A. Albert [I : Two algebras A, B over the same field are called isotopic if there are bijective linear mappings p, u, r from A onto B such that p(x)oj(y) =r(xy) for all x, yEA. In this note we intend to establish the following generalizations of the two theorems mentioned above.