Wedderburn quasialgebras (Q931857)

A Wedderburn quasialgebra is a unital quasialgebra that satisfies the descending chain condition on graded left ideals and with no nonzero nilpotent graded ideals. In this paper an analogue of the Wedderburn-Artin Theorem for quasialgebras is proved. The first result obtained is that if \(A\) is a Wedderburn quasialgebra, then the null part \(A_0\) is a Wedderburn algebra. The main result is the following: Theorem. Let \(A\) be a Wedderburn quasialgebra. Then \(A\) is isomorphic to a finite direct sum of quasialgebras of the form \(\tilde M^\phi_{n_1, \dots, n_r} (\hat D)\), where \(\hat D\) is a division quasi-algebra with cocycle \(\phi\).