Geodesic
Gaussian and Prüfer conditions in bi-amalgamated algebras
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 381-391

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Let $f\colon A\rightarrow B$ and $g\colon A\rightarrow C$ be two ring homomorphisms and let $J$ and $J'$ be ideals of $B$ and $C$, respectively, such that $f^{-1}(J)=g^{-1}(J')$. In this paper, we investigate the transfer of the notions of Gaussian and Prüfer rings to the bi-amalgamation of $A$ with $(B,C)$ along $(J,J')$ with respect to $(f,g)$ (denoted by $A\bowtie ^{f,g}(J,J')),$ introduced and studied by S. Kabbaj, K. Louartiti and M. Tamekkante in 2013. Our results recover well known results on amalgamations in C. A. Finocchiaro (2014) and generate new original examples of rings possessing these properties.
DOI : 10.21136/CMJ.2019.0335-18
Classification : 13A15, 13C10, 13C11, 13D05, 13E05, 13F05, 13F20, 13F30, 16D40, 16E10, 16E60
Keywords: bi-amalgamation; amalgamated algebra; Gaussian ring; Prüfer ring 
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     title = {Gaussian and {Pr\"ufer} conditions in bi-amalgamated algebras},
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     publisher = {mathdoc},
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Mahdou, Najib; Moutui, Moutu Abdou Salam. Gaussian and Prüfer conditions in bi-amalgamated algebras. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 381-391. doi: 10.21136/CMJ.2019.0335-18

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