The Dickson Subcategory Splitting Conjecture for Pseudocompact Algebras

M. C. Iovanov; Constantin Nastasescu; Blas Torrecillas-Jover

The Dickson Subcategory Splitting Conjecture for Pseudocompact Algebras

Category Theory 2011-09-21 v1 Rings and Algebras Representation Theory

Authors: M. C. Iovanov , Constantin Nastasescu , Blas Torrecillas-Jover

Abstract

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.

Keywords

lie algebras associative algebras tensor category

Cite

@article{arxiv.1109.4210,
  title  = {The Dickson Subcategory Splitting Conjecture for Pseudocompact Algebras},
  author = {M. C. Iovanov and Constantin Nastasescu and Blas Torrecillas-Jover},
  journal= {arXiv preprint arXiv:1109.4210},
  year   = {2011}
}

Comments

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

The Dickson Subcategory Splitting Conjecture for Pseudocompact Algebras

Abstract

Keywords

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