# On a notion of "Galois closure" for extensions of rings

## Author(s): Bhargava, Manjul; Satriano, Matthew

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 Abstract: 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 S_n 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. Publication Date: 2014 Electronic Publication Date: 2014 Citation: M. BHARGAVA and M. SATRIANO , On a notion of “Galois closure” for extensions of rings ,J.Eur.Math.Soc.(JEMS) 16 (2014), 1881–1913. MR 3273311. DOI 10.4171/JEMS/478. (1885, 1886) Pages: 1881–1913 Type of Material: Journal Article Journal/Proceeding Title: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY Version: Author's manuscript