Geodesic
On a notion of “Galois closure” for extensions of rings
Journal of the European Mathematical Society, Tome 16 (2014) no. 9, pp. 1881-1913 Cet article a éte moissonné depuis la source EMS Press

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We introduce a notion of “Galois closure” for extensions of rings. We show that the notion agrees with the usual notion of Galois closure in the case of an Sn​ degree n extension of fields. Moreover, we prove a number of properties of this construction; for example, we show that it is functorial and respects base change. We also investigate the behavior of this Galois closure construction for various natural classes of ring extensions
DOI : 10.4171/jems/478
Classification : 11-XX, 13-XX
Keywords: Galois closure, ring extension, field extension, étale extension, monogenic extension, Sn​-representation 
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     author = {Manjul Bhargava and Matthew Satriano},
     title = {On a notion of {{\textquotedblleft}Galois} closure{\textquotedblright} for extensions of rings},
     journal = {Journal of the European Mathematical Society},
     pages = {1881--1913},
     year = {2014},
     volume = {16},
     number = {9},
     doi = {10.4171/jems/478},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/478/}
}
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Manjul Bhargava; Matthew Satriano. On a notion of “Galois closure” for extensions of rings. Journal of the European Mathematical Society, Tome 16 (2014) no. 9, pp. 1881-1913. doi: 10.4171/jems/478

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