A NOTE ON REFLEXIVE RINGS

Mason introduced the reflexive property for ideals and then this concept was generalized by Kim and Baik, defining idempotent reflexive right ideals and rings. In this note we consider reflexive property of a special subring of the infinite upper triangular matrix ring over a ring $R.$ We proved that, if $R$ is a left $APP$-ring, then $V_{n}(R)$ is reflexive. We also give an example which shows that the ring $V_{n}(R)$ need not be left $APP$ when $R$ is a left $APP$-ring.