The Galois closure for rings and some related constructions

2015/02/04 by Alberto Gioia, Gioia, Alberto
Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT) #math.AC #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1502.01210

30 pages

arxiv created 2015/02/04 · arxiv updated 2015/02/05

Abstract

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).

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