The Galois closure for rings and some related constructions

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• 作者：Alberto Gioia ^{alberto.gioia@univie.ac.at" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 13B05 ; 13C10 ; secondary ; 14A05 ; 14B25 ; 11R04
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：446
• 期：Complete
• 页码：450-488
• 全文大小：610 K

文摘

Let R be a ring and let A be a finite projective R-algebra of rank n. Manjul Bhargava and Matthew Satriano have recently constructed an R  -algebra G(A/R)$G(A/R)$, the Galois closure of A/R$A/R$. Many natural questions were asked at the end of their paper. Here we address one of these questions, proving the existence of the natural constructions they call intermediate S_n$S_n$-closures. We will also study properties of these constructions, generalizing some of their results, and proving new results both on the intermediate S_n$S_n$-closures and on G(A/R)$G(A/R)$.