Rafail AlizadeYilmaz Mehmet Demirci2025-10-0620171787-240510.18514/MMN.2016.1566http://dx.doi.org/10.18514/MMN.2016.1566https://gcris.yasar.edu.tr/handle/123456789/6595For 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.Englishproper class of short exact sequences, closure of a proper class, sum of proper classes, closure of a moduleArticle