On generalized fraction and power series properties of $\mathcal{S}$-Noetherian rings

Abstract

In this note, we study the generalized fraction properties and power series properties of $\mathcal{S}$-Noetherian rings. Actually, we investigate two questions proposed in [A. Dabbabi, A. Benhissi, Generalization of the $S$-Noetherian concept, {\it Arch. Math.} (Brno) \textbf{59}(4) (2023) 307-314.]