# An approach to Černý's conjecture via the Wedderburn-Artin Theory.

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Černý's conjecture is one of the most longstanding open problems in the theory of finite automata (stated by Černý in 1964). This conjecture claims that a deterministic finite automaton with *n* states and synchronizing, has always a synchronizing word of length *(n-1)^2*. In this seminar, I am going to show an approach to Černý 's conjecture using the Wedderburn-Artin theory. First I introduce the notion of a radical ideal of a synchronizing automaton, and then the natural notion of semisimple synchronizing automata.