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# Conjugation in a general field watch

1. Is it defined?
2. (Original post by J.F.N)
Is it defined?
Yes - but fields are commutative - so it's very boring!
3. (Original post by RichE)
Yes - but fields are commutative - so it's very boring!
Um, I didn't mean the group theoretic conjugation (i.e. bab-1). I meant conjugation as in, say, complex conjugation.
4. (Original post by J.F.N)
Um, I didn't mean the group theoretic conjugation (i.e. bab-1). I meant conjugation as in, say, complex conjugation.
What would it mean generally? Would you require it to be an order two automorphism of the field K with a non-trivial fixed field F?

If so then no as Z_3 has only the identity for an automorphism.
5. (Original post by RichE)
What would it mean generally? Would you require it to be an order two automorphism of the field K with a non-trivial fixed field F?

If so then no as Z_3 has only the identity for an automorphism.
Ok, I get it. I was just wondering if say, given an inner product on a vector space over a field K, does it make sense to speak of the 'conjugate' of <x,y>. I guess not.
6. (Original post by J.F.N)
Ok, I get it. I was just wondering if say, given an inner product on a vector space over a field K, does it make sense to speak of the 'conjugate' of <x,y>. I guess not.
Inner product spaces are real or complex. So how would the question arise?

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Updated: January 31, 2006
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