nLab
pseudocompact module

Contents

Contents

Definition

A topological module? over a topological ring is pseudocompact if it is isomorphic to the limit in the category of topological modules? of discrete topological modules? of finite length (meaning there is an upper bound on the length of increasing chains of submodules).

Equivalently, a pseudocompact module MM is a complete Hausdorff topological module? that has a basis of neighborhoods of 0 consisting of open submodules PP such that M/PM/P has finite length.

Properties

Any pseudocompact module is a linearly compact module.

References

Pseudocompact modules were introduced in

Last revised on December 24, 2019 at 12:29:28. See the history of this page for a list of all contributions to it.