Keskin, Derya TütüncüOrhan, Nil ErtasF., Patrick SmıthTrıbak, Rachid2024-09-292024-09-2920141300-0098https://search.trdizin.gov.tr/tr/yayin/detay/186864https://hdl.handle.net/20.500.14619/12462The submodule Z(M) = ∩{N | 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(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 ∈ Mod−R | ZR(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/openAccessMatematikArticle657464918686438