ON A GENERALIZATION OF LIFTING MODULES RELATIVE TO A TORSION THEORY

Abstract

Let $\tau = (\cal T, \cal F)$ be a torsion theory and $M$ an $R$-module. $M$ is a $\tau$-lifting module if for any submodule $N$ of $M$ there exists a decomposition $M = A \oplus B$ such that $A \leq N$ and $N \cap B$ is $\tau$-small in $M$. This definition unifies several definitions on generalizations of lifting property of modules. The aim of the present paper is to investigate properties of $\tau$-lifting modules. Various results are developed, many extending known results.