Crumbling modules as injectivity domains

Demirci Y. M.

4th International Conference on Pure and Applied Mathematics, Van, Turkey, 22 - 23 June 2022, pp.74

  • Publication Type: Conference Paper / Summary Text
  • City: Van
  • Country: Turkey
  • Page Numbers: pp.74
  • Abdullah Gül University Affiliated: Yes


Poor modules are introduced in [1] as an opposite of injectivity. The rst wave in this line of research has focused mainly on the rings with no middle class (over which every right module is
either poor or injective). In one of such studies, the authors related the existence of semisimple poor modules to the coincidence of the class of all crumbling modules (exactly locally Noetherian V -modules) and the class of all semisimple modules (see [2]). [3] is one of the papers that consider rings that can have more than one middle class.

In this talk, we focus on the case when there is only one middle class of injectivity domains. Especially, we investigate the properties of the rings that have the class of crumbling modules as their only middle class of injectivity domains.