Year: 2025
Type: article
Abstract: We consider infinite double chains ⋯N−1⊂N0⊂N1⊂⋯ and infinite inverse double chains N0⊂N1⊂N2⊂⋯⋯⊂M2⊂M1⊂M0 of submodules of a module M over a commutative ring R. We shall give conditions under which such chains exist. Examples show that they do not always exist even though M satisfies neither the ascending nor the descending chain conditions. The concepts of m-minimal and m-maximal submodules will be introduced as main tools. Also we shall give conditions under which a Noetherian module is Artinian and conditions under which an Artinian module is Noetherian.
Source: Communications in Algebra
Author: Christian Gottlieb
Institution: Stockholm University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4407593174