Linear topology

In algebra, a linear topology on a left ${\displaystyle A}$-module ${\displaystyle M}$ is a topology on ${\displaystyle M}$ that is invariant under translations and admits a fundamental system of neighborhood of ${\displaystyle 0}$ that consists of submodules of ${\displaystyle M.}$ If there is such a topology, ${\displaystyle M}$ is said to be linearly topologized. If ${\displaystyle A}$ is given a discrete topology, then ${\displaystyle M}$ becomes a topological ${\displaystyle A}$-module with respect to a linear topology.