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