What is an \(\Omega\)-Krull ring? (Q788800)

An \(\Omega\)-Krull ring is defined as the intersection of quasi-local \(\Omega\)-rings, which are symmetric localizations of the ring. The difference between a Marubayashi-Krull ring and an \(\Omega\)-Krull ring is that the authors only assume conditions on twosided ideals. The first problem is to find a symmetric analogue of the Goldie theorems, i.e. to give necessary and sufficient conditions such that a ring R may be embedded in a symmetric localization \(Q_{sym}(R)\) which is a simple ring. The authors limit themselves to prime rings satisfying Formanek's condition, i.e. every nonzero ideal intersects the center nontrivially.