Rings with flat right ideals and distributive rings
A ring \(R\) is called distributive if the lattice of right ideals as well as the lattice of left ideals of \(R\) is distributive. The main result of this paper is a generalization of \textit{C. U. Jensen}'s result [Proc. Am. Math. Soc. 15, 951-954 (1964; Zbl 0135.07902)] for commutative rings: Theorem. A semiprime ring \(R\) which is integral over its center is distributive if and only if the set \(R\setminus P\) is an Ore set for each prime ideal \(P\) of \(R\) and weak gl.\(\dim(R)\leq 1\). Conditions are given which ensure that i) the skew polynomial ring \(R_ 0[x,\phi]\) is distributive and ii) the power series ring \(R_ 0x\) is distributive.
scientific article; zbMATH DE number 3968810
scientific article