Derived decompositions of abelian categories are introduced in internal terms subcategories to construct semi-orthogonal (or Bousfield localizations, or hereditary torsion pairs) various derived categories. We give a sufficient condition for arbitrary have such and show that it is also necessary with enough projectives injectives. For bounded categories, we describe which determined by decompos...

We prove that cellular Noetherian algebras with finite global dimension are split quasi-hereditary over a regular commutative ring Krull and their structure is unique, up to equivalence. In the process, we establish algebra semi-perfect if only ground local ring. give formula determine of (with dimension) in terms finite-dimensional algebras. For general case, upper bounds for finitistic arbitr...

The purpose of this paper is to outline a new approach to the classii-cation of nitely generated indecomposable modules over certain kinds of pullback rings. If R is the pullback of two hereditary noetherian serial rings over a common semi{simple artinian ring, then this classiication can be divided into the classiica-tion of indecomposable artinian modules and those modules over the coordinate...

By a near-ring we mean a right near-ring. J 0 , the right Jacobson radical of type 0, was introduced for near-rings by the first and second authors. In this paper properties of the radical J 0 are studied. It is shown that J 0 is a Kurosh-Amitsur radical KA-radical in the variety of all near-rings R, in which the constant part Rc of R is an ideal of R. So unlike the left Jacobson radicals of ty...

We generalize two major ways of obtaining derived equivalences, the tilting process by Happel, Reiten and Smalø and Happel’s Tilting Theorem, to the setting of finitely presented modules over right coherent rings. Moreover, we extend the characterization of quasi–tilted artin algebras as the almost hereditary ones to all right noetherian rings. We also give a streamlined and general presentatio...

Near-rings considered are right near-rings. In this paper two more radicals, the right Jacobson radicals of type-1(e) and 2(e), are introduced for near-rings. It is shown that they are Kurosh-Amitsur radicals (KAradicals) in the class of all near-rings and are ideal-hereditary radicals in the class of all zero-symmetric near-rings. Different kinds of examples are also presented.