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

Bhargava, Manjul, and Satriano, Matthew. "On a notion of “Galois closure” for extensions of rings." Journal of the European Mathematical Society 016.9 (2014): 1881-1913. <http://eudml.org/doc/277351>.

@article{Bhargava2014,
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.},
author = {Bhargava, Manjul, Satriano, Matthew},
journal = {Journal of the European Mathematical Society},
keywords = {Galois closure; ring extension; field extension; étale extension; monogenic extension; $S_n$-representation; Galois closure; ring extension; field extension; étale extension; monogenic extension; $S_n$-representation},
language = {eng},
number = {9},
pages = {1881-1913},
publisher = {European Mathematical Society Publishing House},
title = {On a notion of “Galois closure” for extensions of rings},
url = {http://eudml.org/doc/277351},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Bhargava, Manjul
AU - Satriano, Matthew
TI - On a notion of “Galois closure” for extensions of rings
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 9
SP - 1881
EP - 1913
AB - 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.
LA - eng
KW - Galois closure; ring extension; field extension; étale extension; monogenic extension; $S_n$-representation; Galois closure; ring extension; field extension; étale extension; monogenic extension; $S_n$-representation
UR - http://eudml.org/doc/277351
ER -