On the transfer of some $t-$locally properties

Authors : Omar OUZZAOUİT, Ali TAMOUSSİT

Pages : 825-832

Doi:10.15672/hujms.766283

View : 15 | Download : 4

Publication Date : 2021-06-07

Article Type : Research Paper

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