Topological Ordered Modules
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, $$0\in\textrm{cl}\left(M^{+}\backslash\{0\}\right)$$ , 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.
Fields of Study & Subjects
Rings
Modules
and Algebras
Advanced Algebra and Logic
Fuzzy and Soft Set Theory
Publication details
- Journal / source
- Lobachevskii Journal of Mathematics
- Publisher
- Pleiades Publishing Ltd
- Volume
- 47
- Issue
- 3
- Pages
- 1009–1019
- Publication date
- 1 March 2026
- Language
- EN