关于Morita对偶和自对偶

On Morita Duality and Self-duality

本文证明了忠实平衡双模_RE_S导出Morita对偶的两个等价条件,由此得到上生成元环的一个新刻划。利用Kraemer的证明方法,本文还证明了有一类上生成元环上的有限正规扩张环具有Morita自对偶,从而推得上生成元环D上的斜半群环R=D*θG具有Morita自对偶,这里G为含单位元的有限半群,θ:G→Aut(D)是半群同态。

This paper proves two equivalent conditions for a faithful balanced bimodule _kEs to induce a Morita duality, and a new characterization of cogenerator rings is obtained. Using a recent proof of Kraemer, it shows that there is a class of finite normalizing extension rings over a cogenerator ring that possess Morita self-duality, and derive that the skew semigroup ring R=D(?)G over a cogenerator ring D has Morita self-duality, where G is a finite semigroup with identity and θ: G→Aut(D) is a semigroup homomorphism.