Gaussian and Prüfer conditions in bi-amalgamated algebras

Najib Mahdou; Moutu Abdou Salam Moutui

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 2, page 381-391
  • ISSN: 0011-4642

Abstract

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Let f : A → B and g : A → 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 ⋈ 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.

How to cite

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Mahdou, Najib, and Moutui, Moutu Abdou Salam. "Gaussian and Prüfer conditions in bi-amalgamated algebras." Czechoslovak Mathematical Journal 70.2 (2020): 381-391. <http://eudml.org/doc/297404>.

@article{Mahdou2020,
abstract = {Let $f\colon A\rightarrow B$ and $g\colon A\rightarrow C$ be two ring homomorphisms and let $J$ and $J^\{\prime \}$ be ideals of $B$ and $C$, respectively, such that $f^\{-1\}(J)=g^\{-1\}(J^\{\prime \})$. 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 $(J,J^\{\prime \})$ with respect to $(f,g)$ (denoted by $A\bowtie ^\{f,g\}(J,J^\{\prime \})),$ 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.},
author = {Mahdou, Najib, Moutui, Moutu Abdou Salam},
journal = {Czechoslovak Mathematical Journal},
keywords = {bi-amalgamation; amalgamated algebra; Gaussian ring; Prüfer ring},
language = {eng},
number = {2},
pages = {381-391},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Gaussian and Prüfer conditions in bi-amalgamated algebras},
url = {http://eudml.org/doc/297404},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Mahdou, Najib
AU - Moutui, Moutu Abdou Salam
TI - Gaussian and Prüfer conditions in bi-amalgamated algebras
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 2
SP - 381
EP - 391
AB - Let $f\colon A\rightarrow B$ and $g\colon A\rightarrow C$ be two ring homomorphisms and let $J$ and $J^{\prime }$ be ideals of $B$ and $C$, respectively, such that $f^{-1}(J)=g^{-1}(J^{\prime })$. 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 $(J,J^{\prime })$ with respect to $(f,g)$ (denoted by $A\bowtie ^{f,g}(J,J^{\prime })),$ 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.
LA - eng
KW - bi-amalgamation; amalgamated algebra; Gaussian ring; Prüfer ring
UR - http://eudml.org/doc/297404
ER -

References

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