On the transfer of some $t-$locally properties

Year 2021, Volume: 50 Issue: 3, 825 - 832, 07.06.2021

Omar Ouzzaouit Ali Tamoussit

https://doi.org/10.15672/hujms.766283

Cited By: 1

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 $D,$ $D[X],$ $D\langle X\rangle,$ $D(X)$ and $D[X]_{N_v}$ are simultaneously $t$-locally P$v$MDs (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 (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

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