Plane modules and distributive rings (Q1335993)

The aim of this paper is to prove the equivalence of the following conditions for a semiprime ring \(R\) which is entire over its center: (1) \(R\) is a right distributive ring (this means that the lattice of right ideals of \(R\) is distributive); (2) \(R\) is a left distributive ring; (3) \(\text{w.gl.dim}(R)\leq 1\) and the set \(R \setminus P\) is a right (or left) Ore set for any prime ideal \(P\) of \(R\).