[Note:I have yet not studied field theory,I am just using it in vector spaces.So my question may look silly.] Suppose $F$ is a field and $F \subset \mathbb C$.Then does $F^3$ contain $(1,0,0),(0,1,0), (0,0,1)$. Can anyone show me if they always exist in $F$ and if yes then how?
Suppose $F$ is a field and $F \subset \mathbb C$.Then does $F^3$ contain $(1,0,0),(0,1,0), (0,0,1)$.
Asked
Active
Viewed 67 times
0
-
1Please refer to the link-https://math.stackexchange.com/questions/1225277/any-subfield-of-mathbbc-must-contain-every-rational-number. – Kishalay Sarkar Aug 24 '19 at 15:56
-
it helped,thanks. – Aug 24 '19 at 15:57
1 Answers
2
A field $F$ contains a neutral element for multiplication and one for addition, say $0$ is the neutral element of addition and $1$ the neutral element of multiplication. So $(1,0,0)$ is in $F^3$ since $1 \in F$ and $0 \in F$. Same argument for the other two vectors.
Riquelme
- 641