Half-tilted Modules And Half-tilted Complexes And Their Generalizations

In this thesis,we study silting modules and silting complexes.We give the classification of silting modules,the new characterizations of silting complexes and their generalizations.The thesis is organized as follows:In Chapter 1,some background and main results are given.In Chapter 2,we study minimal silting modules and minimal cosilting modules.The aim of this chapter is twofold.Firstly,we determine the minimal tilting and minimal cotilting modules over a tame hereditary algebra.We show that a large cotilting module is minimal if and only if it has an adic module as a direct summand.Secondly,we discuss the behaviour of minimality under ring extensions.We show that minimal cosilting modules over a commutative noetherian ring extend to minimal cosilting modules along any flat ring epimorphism.Similar results are obtained for commutative rings of weak global dimension at most 1.In Chapter 3,we construct a new class of complexes and describe its properties.We use this class of complexes to characterize silting complexes.In Chapter 4,we introduce and study the notion of Gorenstein silting complexes.We give the characterization of Gorenstein silting complexes and show its relations with silting complexes.In particular,we also give a su cient condition for a partial Gorenstein silting complex to have a complement.In Chapter 5,we introduce the notion of s-tilting modules with respect to static modules.We give its characterizations and show its relations with tilting modules.In addition,we study the transferable properties of s-tilting modules under ring extensions.