Keskin Tutuncu, DeryaOrhan Ertas, NilSmith, Patrick F.Tribak, Rachid2024-09-292024-09-2920141300-00981303-6149https://doi.org/10.3906/mat-1210-15https://hdl.handle.net/20.500.14619/7502The snbmodule (Z)overbar(M) = boolean AND{N vertical bar M/N is small in its injective hull} was introduced by Talebi and Vanaja in 2002. A ring R is said to have property (P) if (Z)overbar(M) is a direct summand of M for every R-module M. It is shown that a commutative perfect ring R has (P) if and only if R is semisimple. An example is given to show that this characterization is not true for noncommutative rings. We prove that if R is a commutative ring such that the class {M is an element of Mod-R vertical bar <(Z)overbar >(R)(M) = 0} is closed under factor modules, then R has (P) if and only if the ring R is von Neumann regular.eninfo:eu-repo/semantics/openAccessvon Neumann regular ringperfect ring(non)cosingular submoduleArticle10.3906/mat-1210-152-s2.0-848989659946574Q264938WOS:000338003700004Q4