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Results tagged with fields
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user 4149
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].
41
votes
Accepted
Isomorphic general linear groups implies isomorphic fields?
The answer is "yes", see below.
Dieudonné in his book "La géométrie des groupes classiques"
considers the abstract group $SL_n(K)$ for a field $K$, not necessarily commutative,
and writes $PSL_n(K)$ …
- 14.2k
13
votes
1
answer
984
views
Is -1 a sum of 2 squares in a certain field K?
Consider the field of fractions $K$
of the quotient algebra $\mathbb{R}[x,y,z,t]/(x^2+y^2+z^2+t^2+1)$,
where $\mathbb{R}$ is the field of real numbers and $x,y,z,t$ are variables.
Clearly $-1$ is a su …
- 65.4k