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Bull. Korean Math. Soc. 2021; 58(4): 1021-1029

Online first article June 25, 2021      Printed July 31, 2021

https://doi.org/10.4134/BKMS.b200784

Copyright © The Korean Mathematical Society.

$S$-Noetherian in bi-amalgamations

Hwankoo Kim, Najib Mahdou, Youssef Zahir

Hoseo University; Box 2202, University S.M. Ben Abdellah Fez; Mohammed-V University in Rabat

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This paper establishes necessary and sufficient conditions for a bi-amalgamation to inherit the $S$-Noetherian property. The new results compare to previous works carried on various settings of duplications and amalgamations, and capitalize on recent results on bi-amalgamations. Our results allow us to construct new and original examples of rings satisfying the $S$-Noetherian property.

Keywords: $S$-Noetherian, bi-amalgamation, amalgamated duplication of a ring along an ideal

MSC numbers: 13D05, 13D02

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