Endo-Noetherian rings

Abstract

A commutative ring R is said to be endo-Noetherian if the chain of annihilators $${ ann}(a_{1})\subseteq $$$${ ann}(a_{2})\subseteq \cdots $$ stabilizes for each sequence $$(a_{k})_{k}$$ of elements of R (Ndiaye and Gueye in Int J Appl Math 86:871–881, 2013). In this paper, we give equivalent conditions for the power series (resp., polynomial) rings over an Armendariz ring to be endo-Noetherian. We also study several properties of an endo-Noetherian ring. The concept of the amalgamated duplication of R along an ideal $$I, R\bowtie I$$ is studied.