Filters and overrings

Abstract

Let R be an integral domain. It is well known (see Lambek (1971), Stenström (1971)), that idempotent filters of right ideals, torsion radicals and trosio theories are in one-to-one correspondence, but that different idempotent filters F of right ideals may lead to the same rings of quotiens Rf. We have always R ⊃ Rf ⊂Qmax(R). Given this situation one can ask a number of questions. For example: Describe all different idempotent filters for a given ring. Determine all different rings of quotients. When do different filters lead to the same ring of quotients? When are all rings between R and Qmax(R) of the form RF. When is every RF of the form RS−1, where S is an Ore system?