New generalization of the class of H-supplemented modules

Abstract

Let P be a right R-module, where R is a ring with identity. In the present research, a class of modules is described similar to H-μ-supplemented and μ-lifting modules. A module P is called principally H-μ-supplemented if there is a summand L of P such that pR is μ-equivalent to L for every p in P. Additionally, we present an extension of supplemented modules. A module P is considered to be principally μ-supplemented if, for every p in P, pR has a μ-supplement in P. A number of characteristics of these modules are shown, and it is demonstrated that both the P_μ-H-supplemented and P_μ-supplemented modules include the class of principally μ-lifting modules.