The Dickson Subcategory Splitting Conjecture for Pseudocompact Algebras

Abstract

Let $A$ be a pseudocompact (or profinite) algebra, so $A=C^{\ast }$ where $C$ is a coalgebra. We show that the if the semiartinian part (the "Dickson" part) of every $A$-module $M$ splits off in $M$, then $A$ is semiartinian, also giving a positive answer in the case of algebras arising as dual of coalgebras (pseudocompact algebras), to a well known conjecture of Faith.

14p, final version; original paper appeared in J. Algebra 320 (2008), no. 5, 2144-2155

References in corpus (2)

• Symmetric coalgebras
• The finite Rat-splitting for coalgebras