Some Extensions of Endo-Noetherian Rings

In this article, we proceed on the transfer of the left endo-Noetherian property on certain ring extensions. We transfer of the right (left) endo-Noetherian property to the right (left) quotient rings. For a subring T of R and a finite set of indeterminates X, we prove that $T + XR[[X]]$ is left endo-Noetherian if and only if $R[[X]]$ is left endo-Noetherian. In addition, we prove that the subring Λ:=\ f ∈ R[[S,ω]]: f(1) ∈ T \ of the skew generalized power series ring $R[[S, ω]]$ is left endo-Noetherian if and only if $R[[S, ω]]$ is left endo-Noetherian. Also, we study the left endo-Noetherian property over the amalgamated duplication rings R I and R ᶠ J. Finally, we introduce additional results on left endo-Noetherian rings.