Topological Ordered Modules

Identificadores

URI: http://hdl.handle.net/10498/39200

DOI: 10.1134/S1995080225609634

ISSN: 1995-0802

Files
Statistics
Metrics and citations
 
Share
Export
EndNoteBibTexRIS
Metadata
Show full item record
Author/s
García Pacheco, Francisco JavierAuthority UCA; Moreno Frías, María ÁngelesAuthority UCA; Murillo Arcila, MarinaAuthority UCA; Rahbariyan, Sakineh
Date
2026
Department
Matemáticas
Source
Lobachevskii Journal of Mathematics, 2026, Vol. 47, No. 3, pp. 1011–1021
Abstract
Sufficient conditions are found for the order topology on an ordered module over an ordered ring to be a module topology.More concretely, if $M$ is an ordered module over a topological unital ordered ring such that $M^+\neq \{0\}$, $M^+\backslash\{0\}$ is downward directed, $0\in \cl\left(M^+\backslash\{0\}\right)$, and the module ordering is strong, then the order topology is a module topology. Nontrivial examples are provided showing that these sufficient conditions are not necessary.
Subjects
topological ring; topological module; order topology
Collections
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
This work is under a Creative Commons License Attribution-NonCommercial-NoDerivatives 4.0 Internacional