Semi-perfect semi-distributive rings
This article contains a series of results on semi-perfect semi-distributive rings (SPSD-rings) and on some specializations, using the concepts of quiver and prime quiver of such rings. In the introductory part (\S 1) some characterizations of semi-perfect rings are shown and conditions when such rings are semi-distributive are mentioned. The following part (\S 2) is devoted to the study of Noetherian SPSD-rings, describing the form of the associated quivers. The intersection of all natural powers of the Jacobson radical \(R\) of a Noetherian SPSD-ring \(A\) is zero. In the last part (\S 3) the hereditary and semi-hereditary SPSD-rings are investigated, reducing their description to the case of prime semi-hereditary serial rings. For such rings the existence and the form of classical quotient rings is shown.
scientific article; zbMATH DE number 1475287