Semiartinian profinite algebras have nilpotent Jacobson radical.
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.
scientific article; zbMATH DE number 6352046
scientific article