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

Manjul Bhargava, Matthew Satriano

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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 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.

Original languageEnglish (US)
Pages (from-to)1881-1913
Number of pages33
JournalJournal of the European Mathematical Society
Volume16
Issue number9
DOIs
StatePublished - Jan 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Field extension
  • Galois closure
  • Monogenic extension
  • Ring extension
  • S-representation
  • Étale extension

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