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.

See also

• Ordered topological vector space
• Ring of restricted power series – Formal power series with coefficients tending to 0Pages displaying short descriptions of redirect targets
• Topological abelian group – concept in mathematicsPages displaying wikidata descriptions as a fallback
• Topological field – Algebraic structure with addition, multiplication, and divisionPages displaying short descriptions of redirect targets
• Topological group – Group that is a topological space with continuous group action
• Topological module
• Topological ring – ring where ring operations are continuousPages displaying wikidata descriptions as a fallback
• Topological semigroup – semigroup with continuous operationPages displaying wikidata descriptions as a fallback
• Topological vector space – Vector space with a notion of nearness

References

• Bourbaki, N. (1972). Commutative algebra (Vol. 8). Hermann.