The structure of rings in which the intersection of inessential prime ideals is zero (Q1580444)

A ring is called an L-ring if the intersection of inessential prime ideals is zero. In this paper, the author characterizes the structure of L-rings and shows that the most of the preceding results due to Goldie, Levy, Rowen, and Kishimoto-Kurata can be obtained through his discussion. As a result, the structure of involutions and derivations of L-rings is also obtained. Finally, the structure of right nonsingular semiprime rings \(R\) in which every nonzero ideal contains a uniform right ideal of \(R\) is investigated and it is shown that the maximal right quotient ring of \(R\) is isomorphic to \(\prod_\alpha\Hom_{D_\alpha}(V_\alpha,V_\alpha)\) where \(D_\alpha\) is a division ring and \(V_\alpha\) is a vector space.