The Galois closure for rings and some related constructions

JOURNAL OF ALGEBRA

卷:446

Article

Gioia, Alberto¹ 

[1] Univ Vienna, Fak Math, A-1010 Vienna, Austria

关键词: Galois closure;    Algebra of finite rank;    Finite etale algebra;    Monogenic algebra;    Splitting algebra;   

DOI  :  10.1016/j.jalgebra.2015.09.027

来源: Elsevier

【 摘 要 】

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), the Galois closure of 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-closures. We will also study properties of these constructions, generalizing some of their results, and proving new results both on the intermediate S-n-closures and on G(A/R). (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free