$S$-Noetherian in bi-amalgamations
Bull. Korean Math. Soc. 2021 Vol. 58, No. 4, 1021-1029
Published online June 25, 2021
Printed July 31, 2021
Hwankoo Kim, Najib Mahdou, Youssef Zahir
Hoseo University; Box 2202, University S.M. Ben Abdellah Fez; Mohammed-V University in Rabat
Abstract : 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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