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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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