A pseudocompact ring is a complete Hausdorff topological ring, , which admits a base at of two-sided open ideals for each of which is an Artinian ring. Equivalently, it is a regular pro-object in Artinian rings.
More generally let be a commutative pseudocompact ring. A complete Hausdorff topological ring will be called a pseudocompact algebra over if
(i) is an algebra in the usual sense, and
(ii) admits a system of open neighbourhoods of 0 consisting of two-sided ideals such that has finite length as an module.
Grothendieck developed the theory of formal groups over pseudocompact rings.
The completed group algebras of profinite groups are naturally pseudocompact algebras, usually considered over finite fields or the profinite completion of the ring of integers.
The homological algebra of such rings and the corresponding modules are discussed in
Last revised on April 7, 2014 at 00:14:40. See the history of this page for a list of all contributions to it.