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

Manjul Bhargava; Matthew Satriano

doi:10.4171/JEMS/478

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

Manjul Bhargava, Matthew Satriano

Research output: Contribution to journal › Article › peer-review

10 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 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.

Original language	English (US)
Pages (from-to)	1881-1913
Number of pages	33
Journal	Journal of the European Mathematical Society
Volume	16
Issue number	9
DOIs	https://doi.org/10.4171/JEMS/478
State	Published - 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

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

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10.4171/JEMS/478

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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 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.",

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AU - Bhargava, Manjul

AU - Satriano, Matthew

N1 - Publisher Copyright: © European Mathematical Society 2014

PY - 2014

Y1 - 2014

N2 - 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.

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 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.

KW - Field extension

KW - Galois closure

KW - Monogenic extension

KW - Ring extension

KW - S-representation

KW - Étale extension

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JF - Journal of the European Mathematical Society

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ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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