Quotient Full Linear Rings

Abstract

We define a ring $R$ to be an FL (full linear) ring if $R$ is isomorphic to the full ring of linear transformations of a left vector space over a division ring. $R$ is QFL if its left maximal quotient ring is an FL ring. In this paper we give necessary and sufficient conditions for a ring to be a QFL ring. We also generalize some results of Chase and Faith concerning subdirect sum decompositions of rings whose left maximal quotient ring is the direct product of FL rings.