On the transfer of some $t-$locally properties

In this paper, we study the transfer of some $t$-locally properties which are stable under localization to $t$-flat overrings an integral domain $D$. We show that $D,$ $D[X],$ $D\langle X\rangle,$ $D(X)$ and $D[X]_{N_v}$ simultaneously P$v$MDs (resp., Krull, G-GCD, Noetherian, Strong Mori). A complete characterization when a pullback is P$v$MD GCD, Mori, Mori) given. As corollaries, investigate among domains form $D+XK[X]$, $D+XK[[X]]$ amalgamated algebras. particular attention devoted almost Krull locally closure having same property.