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Results tagged with fields
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user 1849
Fields as algebraic objects. For vector and tensor fields, use eg. [dg.differential-geometry]. For physical fields, use eg. [mp.mathematical-physics] or [quantum-field-theory].
2
votes
2
answers
162
views
Formulas for the structure constants of a field extension basis given by a primitive element
I have looked into J.S.Milne's notes on Fields and Galois Theory and on Algebraic Number Theory as well as in Neukirch's Algebraic Number Theory, but in this regard they don't seem to go beyond calculating …
- 7,127
1
vote
Accepted
Formulas for the structure constants of a field extension basis given by a primitive element
I am not entirely sure on the policy of answering one's own question, I am posting this for the sake of completeness and closure for anyone who might be interested in the same question.
Following Ofi …
- 7,127
22
votes
Accepted
Are there only two smooth manifolds with field structure: real numbers and complex numbers?
Here is a series of standard arguments.
Let $(\mathbb{F},+,\star)$ be such a field. Then $(\mathbb{F},+)$ is a finite-dimensional (path-)connected abelian Lie group, hence $(\mathbb{F},+) \cong \mathb …
- 7,127
4
votes
transcendental Galois theory
The latter corresponds to your definition of Galois extension for arbitrary fields. …
- 7,127