Modüllerin Dik Toplamlarının İnjektifliğinin Kapsamı

Abstract

In this thesis, we present a method inspired by the fact that a ring is a right Noetherian ring if and only if the direct sums of injective right modules is injective, which is introduced in recent studies to show how the injectivity domains of certain modules can serve to measure the extent to which a ring is Noetherian. The notions of stable injectivity domains, stable modules and Noetherian threshold, which are defined for this purpose, are presented. Some characterizations of volatile rings, which are introduced as a notion opposite to Noetherianness, examples of volatile rings and examples of rings that are neither Noetherian nor volatile are given.