Semiartinian Profinite Algebras have Nilpotent Jacobson Radical

Miodrag Iovanov

doi:10.1007/s10468-013-9438-7

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Semiartinian Profinite Algebras have Nilpotent Jacobson Radical

Journal article

Peer reviewed

Semiartinian Profinite Algebras have Nilpotent Jacobson Radical

Miodrag Iovanov

Algebras and Representation Theory, Vol.17(4), pp.1145-1154

08/2014

DOI: 10.1007/s10468-013-9438-7

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https://arxiv.org/pdf/1512.09338View

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Abstract

We give a method to study the finiteness of the coradical filtration of a coalgebra; as a consequence, we show that a left semiartinian profinite algebra has nilpotent Jacobson radical and is right semiartinian too. Equivalently, we show that a for a semilocal profinite algebra, T-nilpotence implies nilpotence for the Jacobson radical. This answers two open questions from Iovanov et al. (J Algebra 320(5):2144–2155, 2008).

Mathematics

Torsion theory

Non-associative Rings and Algebras

Commutative Rings and Algebras

Associative Rings and Algebras

Coalgebra

Splitting

Semiartinian

18E40

Coradical filtration

16T05

Rational module

Profinite algebra

16T15

Details

Title: Subtitle: Semiartinian Profinite Algebras have Nilpotent Jacobson Radical
Creators: Miodrag Iovanov - Faculty of Mathematics University of Bucharest Str. Academiei 14 010014 Bucharest Romania
Resource Type: Journal article
Publication Details: Algebras and Representation Theory, Vol.17(4), pp.1145-1154
DOI: 10.1007/s10468-013-9438-7
ISSN: 1386-923X
eISSN: 1572-9079
Publisher: Springer Netherlands; Dordrecht
Language: English
Date published: 08/2014
Academic Unit: Mathematics
Record Identifier: 9983985802802771

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