Object-unital groupoid graded rings, crossed products and separability

被引：4
作者：
Cala, Juan [1 ]
Lundstrom, Patrik [2 ]
Pinedo, Hector [1 ]
机构：
[1] Univ Ind Santander, Escuela Matemat, Bucaramanga, Colombia
[2] Univ West, Dept Engn Sci, SE-46186 Trollhattan, Sweden
来源：
COMMUNICATIONS IN ALGEBRA | 2021年 / 49卷 / 04期
关键词：
Crossed product; graded ring; groupoids; separable extension;
D O I：
10.1080/00927872.2020.1846742
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：1676 / 1696
页数：21
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