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Semiartinian Profinite Algebras have Nilpotent Jacobson Radical

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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).

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Authors and Affiliations

  1. Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA, 52242-1419, USA

    Miodrag Cristian Iovanov

  2. Faculty of Mathematics, University of Bucharest, Str. Academiei 14, 010014, Bucharest, Romania

    Miodrag Cristian Iovanov

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  1. Miodrag Cristian Iovanov
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Correspondence to Miodrag Cristian Iovanov.

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Presented by Alain Verschoren and Peter Littelmann.

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Iovanov, M.C. Semiartinian Profinite Algebras have Nilpotent Jacobson Radical . Algebr Represent Theor 17, 1145–1154 (2014). https://doi.org/10.1007/s10468-013-9438-7

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  • DOI: https://doi.org/10.1007/s10468-013-9438-7

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