JournalsjemsVol. 16, No. 9pp. 1881–1913

On a notion of “Galois closure” for extensions of rings

  • Manjul Bhargava

    Princeton University, United States
  • Matthew Satriano

    University of Michigan, Ann Arbor, USA
On a notion of “Galois closure” for extensions of rings cover
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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 SnS_n degree nn 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

Cite this article

Manjul Bhargava, Matthew Satriano, On a notion of “Galois closure” for extensions of rings. J. Eur. Math. Soc. 16 (2014), no. 9, pp. 1881–1913

DOI 10.4171/JEMS/478