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Results tagged with fields
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user 12858
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].
5
votes
The integral closure $\overline{\mathbb{Z}}$ and the group $\overline{\mathbb{Z}}^{\times}$
The ring $\overline{\mathbb{Z}}$ is called the ring of algebraic integers. You can find information about prime ideals, e.g., in https://math.stackexchange.com/questions/156231/non-zero-prime-ideals-i …
- 6,614
4
votes
Accepted
Subfields of division rings of degree $2$ which are not invariant
(This is basically a more detailed version of Eoin's comment.)
I assume that you are considering division algebras over a field $k$, i.e., $Z(A) = k$. If $B$ is a subalgebra of dimension $2$ of $A$, t …
- 6,614
3
votes
Heisenberg-type groups over rings with involution
that you mention, but I have used the group $A$ that you described in the case where $R$ is an octonion division algebra, in order to describe the rank one forms of groups of type $F_4$ (over arbitrary fields …
- 6,614