Semiartinian profinite algebras have nilpotent Jacobson radical.
type: Item
instance of: scholarly article
title: Semiartinian profinite algebras have nilpotent Jacobson radical.
zbMATH Open document ID: 1311.16030
author: Miodrag Cristian Iovanov
published in: Algebras and Representation Theory
publication date: 2014-10-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1512.09338
review text: Let \(C\) be a coalgebra and \(C^*\) the associated convolution dual algebra. In this paper, the author answers two interesting problems about the structure of coalgebras. It is shown that if \(C^*\) is a left semiartianian ring then \(C\) has a finite coradical filtration. As a consequence any left semiartinian profinite algebra \(A\) has a nilpotent Jacobson radical, \(A/\mathrm{Jac}(A)\) is finite dimensional semisimple and it is right semiartinian as well.
Mathematics Subject Classification ID: 16T15
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 16N20
Mathematics Subject Classification ID: 16P20
Mathematics Subject Classification ID: 16S90
zbMATH DE Number: 6352046
zbMATH Keywords: profinite algebras
zbMATH Keywords: coalgebras
zbMATH Keywords: coradical filtrations
zbMATH Keywords: splitting torsion theories
zbMATH Keywords: rational modules
zbMATH Keywords: semiartinian rings
reviewed by: Blas Torrecillas
MaRDI profile type: Publication
OpenAlex ID: W2963708226
arXiv ID: 1512.09338
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DOI: 10.1007/S10468-013-9438-7
description: scientific article; zbMATH DE number 6352046