pseudocompact module

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.

Any pseudocompact module is a linearly compact module.

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

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