In
algebra
Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...
, a linear topology on a left
-module
is a
topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...
on
that is invariant under translations and admits a fundamental system of neighborhood of
that consists of submodules of
If there is such a topology,
is said to be linearly topologized. If
is given a discrete topology, then
becomes a
topological -module with respect to a linear topology.
See also
*
*
*
*
*
*
*
*
*
References
* Bourbaki, N. (1972). Commutative algebra (Vol. 8). Hermann.
Topology
Topological algebra
Topological groups
{{algebra-stub