$FI$-$t$-Lifting Modules and $T$-Quasi-Dual Baer Modules

Abstract:

      The notions of $FI$-$t$-lifting modules and $t$-quasi-dual Baer modules are introduced and the relations between them are studied in this paper. It is shown that an amply supplemented module $M$ is an $FI$-$t$-lifting module if and only if every fully invariant $t$-coclosed submodule of $M$ is a direct summand of $M$ if and only if $\bar{Z}^{2}(M)$ is a direct summand of $M$ and $\bar{Z}^{2}(M)$ is an $FI$-lifting module if and only if $M$ is $t$-quasi-dual Baer and an $FI$-$t$-$\mathcal{K}$-module.