Journal of the European Mathematical Society


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Volume 16, Issue 9, 2014, pp. 1881–1913
DOI: 10.4171/JEMS/478

Published online: 2014-10-22

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

Manjul Bhargava[1] and Matthew Satriano[2]

(1) Princeton University, United States
(2) University of Michigan, Ann Arbor, USA

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

Keywords: Galois closure, ring extension, field extension, étale extension, monogenic extension, $S_n$-representation

Bhargava Manjul, Satriano Matthew: On a notion of “Galois closure” for extensions of rings. J. Eur. Math. Soc. 16 (2014), 1881-1913. doi: 10.4171/JEMS/478