Multiplicative basis for algebras whose universal cover has no oriented cycles (Q792431)

The authors prove that if a universal cover of a finite-dimensional algebra over an algebraically closed field of finite representation type has no oriented cycles, then the algebra has a multiplicative basis. For this class of algebras, it gives a proof of the validity of Gabriel's conjecture saying that for each dimension, there exists only a finite number of non-isomorphic algebras of finite representation type.