Artinian rings with Morita duality (Q1286712)

The author investigates Artinian rings with duality in terms of finite triangular generation, which allows an extension of Azumaya's theorem on the duality of exact rings. Examples are given to show that factor rings of QF-rings are not necessarily selfdual and Artinian local left duo rings need not admit duality. Reviewer's remark: If a semisimple Artinian ring \(R\) is finitely generated over its center \(Z\), then \(Z\) is also semisimple Artinian by a theorem of Eisenbud and Robson, and hence \(R\) is a PI-ring. Therefore if \(R\) is an Artinian ring whose semisimple factor is finitely generated over the center, then \(R\) is also a PI-ring, consequently \(R\) has duality by a result of Rosenberg and Zelinsky. This observation answers Questions 1, 2 and simplifies some results of the paper.