LIFTING MODULES WITH RESPECT TO A PRERADICAL

Abstract

Let $M$ be a right module over a ring $R$, $tau_M$ a preradical on $sigma[M]$, and $Ninsigma[M]$. In this note we show that if $N_1, N_2in sigma[M]$ are two $tau_M$-lifting modules such that $N_i$ is $N_j$-projective ($i,j=1,2$), then $N=N_1oplus N_2$ is $tau_M$-lifting. We investigate when homomorphic image of a $tau_M$-lifting module is $tau_M$-lifting.