The Dickson Subcategory Splitting Conjecture for Pseudocompact Algebras

Details The Dickson Subcategory Splitting Conjecture for Pseudocompact Algebras The Dickson Subcategory Splitting Conjecture for Pseudocompact Algebras

2011-09-20

arxiv.org/abs/1109.4210v1

J. Algebra 320 (2008), no. 5, 2144-2155

Mathematics

Category Theory

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

Scientific paper

Let $A$ be a pseudocompact (or profinite) algebra, so $A=C^*$ 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.

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