Czechoslovak Mathematical Journal, first online, pp. 1-11


Gaussian and Prüfer conditions in bi-amalgamated algebras

Najib Mahdou, Moutu Abdou Salam Moutui

Received July 14, 2018.   Published online December 5, 2019.

Abstract:  Let $f A\rightarrow B$ and $g A\rightarrow C$ 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.
Keywords:  bi-amalgamation; amalgamated algebra; Gaussian ring; Prüfer ring
Classification MSC:  13F05, 13A15, 13E05, 13F20, 13C10, 13C11, 13F30, 13D05, 16D40, 16E10, 16E60
DOI:  10.21136/CMJ.2019.0335-18

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Affiliations:   Najib Mahdou, Modelling and Mathematical Structures Laboratory, Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, Sidi Mohamed Ben Abdellah University, Fez, Morocco e-mail: mahdou@hotmail.com; Moutu Abdou Salam Moutui (corresponding author), Department of Mathematics, College of Science, King Faisal University, PO Box 400, Al Hofuf, Al-Ahsa 31982, Saudi Arabia, e-mail: mmoutui@kfu.edu.sa


 
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