Skew Polynomials and Algebraic Reflexivity

This is the authors' abstract. We don't add key points for this paper.

For an arbitrary K-algebra R, an R, K-bimodule M is algebraically reflexive if the only K-endomorphisms of M leaving invariant every R-submodule of M are the scalar multiplications by elements of R. Hadwin has shown for an infinite field K and R = K[x] that R is reflexive as an R, K-bimodule. This paper provides a generalisation by giving a skew polynomial version of his result.