nLab pseudocompact module

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 $M$ is a complete Hausdorff topological module? that has a basis of neighborhoods of 0 consisting of open submodules $P$ such that $M/P$ has finite length.

Properties

Any pseudocompact module is a linearly compact module.

Related concepts

• linearly compact module

• pseudocompact ring

References

Pseudocompact modules were introduced in

• Pierre Gabriel, Des catégories abéliennes,

  Bulletin de la S. M. F., tome 90 (1962), 323-448, http://www.numdam.org/item?id=BSMF_1962__90__323_0