Document Type: Original Manuscript


Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran, Babolsar, Iran


In this paper we introduce the notions of $G_{1}^{*}L$-module and $G_{2}^{*}L$-module which are two proper generalizations of $\delta$-lifting modules. We give some characterizations and properties of these modules. We show that a
$G_{2}^{*}L$-module decomposes into a semisimple submodule $M_{1}$ and a submodule $M_{2}$ of $M$ such that every non-zero submodule of $M_{2}$ contains a non-zero $\delta$-cosingular submodule.