%0 Journal Article 
%A García Pacheco, Francisco Javier
%A Moreno Frías, María Ángeles
%A Murillo Arcila, Marina
%A Rahbariyan, Sakineh
%T Topological Ordered Modules
%D 2026
%@ 1995-0802
%U http://hdl.handle.net/10498/39200
%X 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.
%K topological ring
%K topological module
%K order topology
%~ Universidad de Cádiz