Alizade, RafailDemirci, Yilmaz Mehmet2025-03-232025-03-2320171787-24051787-2413https://doi.org/10.18514/MMN.2016.1566https://hdl.handle.net/11486/4922For an integral domain R we consider the closures (M) over cap ((M) over cap (r), r epsilon R) of a submodule M of an R-module N consisting of elements n of N with t n epsilon M (r(m) n epsilon M) for some nonzero t epsilon R (m epsilon Z(+)) and its connections with usual closure (M) over bar of M in N. Using these closures we study the closures (P) over cap and (P) over cap (r) 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 (P) over cap (G)(F) is a proper classes.eninfo:eu-repo/semantics/closedAccessproper class of short exact sequencesclosure of a proper classsum of proper classesclosure of a moduleArticle17272373810.18514/MMN.2016.15662-s2.0-85014688581Q2WOS:000396217100002Q2