Ring epimorphisms often induce silting modules and cosilting modules, termed minimal or cosilting. The aim of this paper is twofold. Firstly, we determine the tilting cotilting over a tame hereditary algebra. In particular, show that large module if only it has an adic as direct summand. Secondly, discuss behavior minimality under ring extensions. We commutative noetherian extend to along any f...

An R-module is called semi-endosimple if it has no proper fully invariant essential submodules. For a quasi-projective retractable module MR we show that M is finitely generated semi-endosimple if and only if the endomorphism ring of M is a finite direct sum of simple rings. For an arbitrary module M , conditions equivalent to the semi-endosimplicity of its quasi-injective hull are found. As co...

Atropine has been used to block cholinergic neurotransmission in basic research. Large doses of atropine cause vasodilation of the blood vessels in the skin. This effect is apparently unconnected with the antimuscarinic activity of atropine and seems to be due to a direct action on the blood vessels. It has been suggested that atropine blocks muscarinic receptors at low doses and it induces th...

Notations and conventions 296 Introduction 296 I. Serre duality and almost split sequences 300 I.1. Preliminaries on Serre duality 300 I.2. Connection between Serre duality and Auslander–Reiten triangles 304 I.3. Serre functors on hereditary abelian categories 307 II. Hereditary noetherian abelian categories with non-zero projective objects 309 II.1. Hereditary abelian categories constructed fr...

The characterization by J. Levitzki of the prime radical of an associative ring R as the set of strongly nilpotent elements of R is adapted here to apply to a wide class of nonassociative rings. As a consequence it is shown that the prime radical is a hereditary radical for the class of alternative rings and that the prime radical of an alternative ring coincides with the prime radical of its a...