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## On the transfer of some $t-$locally properties

#### Omar OUZZAOUİT [1] , Ali TAMOUSSİT [2]

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.
$t$--Flat overring, ($t$--)Nagata ring, Serre conjecture ring, pullback construction
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Primary Language en Mathematics Mathematics Orcid: 0000-0001-6827-4022Author: Omar OUZZAOUİT (Primary Author)Institution: Ibn Zohr UniversityCountry: Morocco Orcid: 0000-0003-1078-0250Author: Ali TAMOUSSİTInstitution: The Regional Center for Education and Training Professions Souss MassaCountry: Morocco Publication Date : June 7, 2021
 Bibtex @research article { hujms766283, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2021}, volume = {50}, pages = {825 - 832}, doi = {10.15672/hujms.766283}, title = {On the transfer of some \$t-\$locally properties}, key = {cite}, author = {Ouzzaouit, Omar and Tamoussit, Ali} } APA Ouzzaouit, O , Tamoussit, A . (2021). On the transfer of some $t-$locally properties . Hacettepe Journal of Mathematics and Statistics , 50 (3) , 825-832 . DOI: 10.15672/hujms.766283 MLA Ouzzaouit, O , Tamoussit, A . "On the transfer of some $t-$locally properties" . Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 825-832 Chicago Ouzzaouit, O , Tamoussit, A . "On the transfer of some $t-$locally properties". Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 825-832 RIS TY - JOUR T1 - On the transfer of some $t-$locally properties AU - Omar Ouzzaouit , Ali Tamoussit Y1 - 2021 PY - 2021 N1 - doi: 10.15672/hujms.766283 DO - 10.15672/hujms.766283 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 825 EP - 832 VL - 50 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.766283 UR - https://doi.org/10.15672/hujms.766283 Y2 - 2021 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics On the transfer of some $t-$locally properties %A Omar Ouzzaouit , Ali Tamoussit %T On the transfer of some $t-$locally properties %D 2021 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 50 %N 3 %R doi: 10.15672/hujms.766283 %U 10.15672/hujms.766283 ISNAD Ouzzaouit, Omar , Tamoussit, Ali . "On the transfer of some $t-$locally properties". Hacettepe Journal of Mathematics and Statistics 50 / 3 (June 2021): 825-832 . https://doi.org/10.15672/hujms.766283 AMA Ouzzaouit O , Tamoussit A . On the transfer of some $t-$locally properties. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 825-832. Vancouver Ouzzaouit O , Tamoussit A . On the transfer of some $t-$locally properties. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 825-832. IEEE O. Ouzzaouit and A. Tamoussit , "On the transfer of some $t-$locally properties", Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, pp. 825-832, Jun. 2021, doi:10.15672/hujms.766283

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