Ceken Gezen, Secil2024-06-122024-06-1220200092-78721532-4125https://doi.org/10.1080/00927872.2020.1768266https://hdl.handle.net/20.500.14551/22317In this article, we introduce the notion of M-coidempotent elements of a ring and investigate their connections with fully coidempotent modules, fully copure modules and vn-regular modules where M is a module. We prove that if M is a finitely cogenerated module, then M is fully copure if and only if M is semisimple. We prove that if M is a Noetherian module or M is a finitely cogenerated module, then M is fully coidempotent if and only if M is a vn-regular module. Finally, we give a characterization of semisimple Artinian modules via weak idempotents.en10.1080/00927872.2020.1768266info:eu-repo/semantics/closedAccessM-Coidempotent ElementFully Coidempotent ModuleFully Copure ModuleVn-Regular ModuleComultiplication ModulesDual NotionRingsArticle481146384646Q3WOS:0005389342000012-s2.0-85085969591Q2