论文标题
对象 - 非对象 - 分组级别的环，交叉产品和可分离性
Object-unital groupoid graded rings, crossed products and separability
论文作者
论文摘要
我们通过有限的Galois场扩展定义的越野代数来扩展经典的结构，以覆盖可分离（但不一定是有限或正常）场扩展的情况。这很自然地考虑了我们称之为对象Unital的特定类型的非突起群体级环。我们确定何时对这种环进行了强烈的分级，交叉产物，偏斜的类固醇环和扭曲的类固醇环。我们还获得了必要的和足够的标准，即当对象Unital group渐变环在其主要成分上可分开时，从而将Unital Case的先前结果推广到非阴性情况。
We extend the classical construction by Noether of crossed product algebras, defined by finite Galois field extensions, to cover the case of separable (but not necessarily finite or normal) field extensions. This leads us naturally to consider non-unital groupoid graded rings of a particular type that we call object unital. We determine when such rings are strongly graded, crossed products, skew groupoid rings and twisted groupoid rings. We also obtain necessary and sufficient criteria for when object unital groupoid graded rings are separable over their principal component, thereby generalizing previous results from the unital case to a non-unital situation.
