Some Extensions of Endo-Noetherian Rings
R. M. Salem, R. E. Abdel-Khalek, and N. Abdelnasser

TL;DR
This paper investigates how the left endo-Noetherian property transfers to various ring extensions, including power series rings, skew generalized power series rings, and amalgamated duplication rings, providing necessary and sufficient conditions.
Contribution
It establishes new criteria for the transfer of the left endo-Noetherian property to several classes of ring extensions, expanding understanding of this property in ring theory.
Findings
Transfer of left endo-Noetherian property to power series rings is characterized.
Subring conditions for endo-Noetherian property in skew generalized power series rings are established.
Results on endo-Noetherian property in amalgamated duplication rings are provided.
Abstract
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 of and a finite set of indeterminates , we prove that is left endo-Noetherian if and only if is left endo-Noetherian. In addition, we prove that the subring of the skew generalized power series ring is left endo-Noetherian if and only if is left endo-Noetherian. Also, we study the left endo-Noetherian property over the amalgamated duplication rings and . Finally, we introduce additional results on left endo-Noetherian rings.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Algebraic structures and combinatorial models
