Refail AlizadeYılmaz Mehmet DemirciAlizade, RafailDemirci, Yilmaz Mehmet2025-10-06201617872413, 178724051787-24051787-241310.18514/MMN.2016.15662-s2.0-85014688581https://www.scopus.com/inward/record.uri?eid=2-s2.0-85014688581&doi=10.18514%2FMMN.2016.1566&partnerID=40&md5=3361b60ec6732f7588c7c9b9cbf9bf0dhttps://gcris.yasar.edu.tr/handle/123456789/9828https://doi.org/10.18514/MMN.2016.1566For an integral domain R we consider the closures M (Mr r ε R) of a submodule M of an R-module N consisting of elements n of N with tn 2 M (rmn ε M) for some nonzero t ε R (m ε Z+) and its connections with usual closure M of M in N. Using these closures we study the closures P and Pr of a proper class P of short exact sequences and give a decomposition for the class of quasi-splitting short exact sequences of abelian groups into the direct sum of "p-closures" of the class Split of splitting short exact sequences and description of closures of some classes. In the general case of an arbitrary ring we generalize these closures of a proper class P by means of homomorphism classes F and G and prove that under some conditions this closure is a propier classes. © 2020 Elsevier B.V. All rights reserved.Englishinfo:eu-repo/semantics/closedAccessClosure Of A Module, Closure Of A Proper Class, Proper Class Of Short Exact Sequences, Sum Of Proper ClassesClosure of a ModuleProper Class of Short Exact SequencesSum of Proper ClassesClosure of a Proper ClassArticle