Bagio and Paques [Partial groupoid actions: globalization, Morita theory and Galois theory, Comm. Algebra 40 (2012) 3658–3678] developed a Galois theory for unital partial actions by finite groupoids. The aim of this note is to show that this is actually a special case of the Galois theory for corings, as introduced by Brzeziński [The structure of corings, Induction functors, Maschke-type theorem, and Frobenius and Galois properties, Algebr. Represent. Theory 5 (2002) 389–410]. To this end, we associate a coring to a unital partial action of a finite groupoid on an algebra [Formula: see text], and show that this coring is Galois if and only if [Formula: see text] is an [Formula: see text]-partial Galois extension of its coinvariants.

中文翻译：

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部分作用于代数的伽罗瓦核和群

Bagio 和 Paques [部分群行为：全球化，森田理论和伽罗瓦理论，Comm。Algebra 40 (2012) 3658–3678] 开发了有限群的单位部分作用的伽罗瓦理论。本说明的目的是表明这实际上是由 Brzeziński [The structure of corings, Induction functors, Maschke-type theorem, and Frobenius and Galois properties, Algebr. 代表。理论 5 (2002) 389–410]。为此，我们将核化与代数[公式：见文本]上的有限群的单位部分作用相关联，并证明当且仅当[公式：见文本]是[公式：见文本]时，该核化是伽罗瓦text]-其协变式的部分伽罗瓦扩展。