  The impetus for this study is the work of Dumas and Rigal on the Jordanian
deformation of the ring of coordinate functions on $2\times 2$ matrices. We are
also motivated by current interest in birational equivalence of noncommutative
rings. Recognizing the construction of the Jordanian matrix algebra as a skew
polynomial ring, we construct a family of algebras relative to differential
operator rings over a polynomial ring in one variable which are birationally
equivalent to the Weyl algebra over a polynomial ring in two variables.
