If is a finite algebraic extension, it can be defined by a polynomial . The polynomial discriminant, , is well-defined up a factor of a non-zero square. The discriminant root field of the extension is , which is well-defined.
If , then the Galois group for is a subgroup of , well-defined up to conjugation. The discriminant root field can alternatively be described as the fixed field of .
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- Last edited by David Roe on 2024-04-13 10:36:47
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- 2024-04-13 10:36:47 by David Roe (Reviewed)
- 2023-04-07 13:17:08 by John Jones (Reviewed)