ε-强分次环，分离性和半单性
Epsilon-strongly graded rings, separability and semisimplicity
摘要：
引入了ε-强分次环类，并证明了它适当地包含强分次环类和单位部分交叉积类.精确地确定了ε-强分次环在其主成分上可分的条件。从而，我们同时推广了Nastasescu，Van den Bergh和Van Oystaeyen关于强群分次分次环的一个结果和Bagio，Lazzarin和Paques关于单位部分交叉积的一个结果.我们还表明，类的单位部分交叉产品出现在类的ε-强分次环的方式类似于如何经典交叉产品目前自己在类的强分次环。从而，在单位部分交叉积的特殊情况下，得到了Dokuchaev，Exel和Simón关于分次环何时可表示为部分交叉积的一般结果的一个简短证明.我们还提供了一些有趣的例子类的可分ε-强分次环，有限以及无限分次群。特别是，我们得到了一个问题的答案提出的Le Bruyn，Van den Bergh和Van Oystaeyen在1988年。
英文摘要：
We introduce the class of epsilon-strongly graded rings and show that it properly contains both the class of strongly graded rings and the class of unital partial crossed products. We determine precisely when an epsilon-strongly graded ring is separable over its principal component. Thereby, we simultaneously generalize a result for strongly group graded rings by Nastasescu, Van den Bergh and Van Oystaeyen, and a result for unital partial crossed products by Bagio, Lazzarin and Paques. We also show that the class of unital partial crossed products appear in the class of epsilon-strongly graded rings in a fashion similar to how the classical crossed products present themselves in the class of strongly graded rings. Thereby, we obtain, in the special case of unital partial crossed products, a short proof of a general result by Dokuchaev, Exel and Simón concerning when graded rings can be presented as partial crossed products. We also provide some interesting classes of examples of separable epsilon-strongly graded rings, with finite as well as infinite grading groups. In particular, we obtain an answer to a question raised by Le Bruyn, Van den Bergh and Van Oystaeyen in 1988.
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