Endo-Noetherian Skew Generalized Power Series Rings

Abstract

In this article, denotes a ring with identity (not necessarily to be commutative). A. Kaidi and E. Sanchez [1] introduced a new class of rings called endo-Noetherian rings as a generalization of Noetherian rings which was identified by Emmy Noether in 1921 [2] and the name Noetherian is in her honor. Also, the endo-Noetherian property is a generalization of the iso-Noetherian property (see Definition 3). A left -module is called endo-Noetherian if any ascending chain of endomorphic kernels Ker ( ) ⊆ Ker ( ) ⊆ ..., stabilizes, where ∈ End ( ) for all , i.e., there exists uch that