Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $F=\mathbb{Q}(\sqrt{-d})$ be an imaginary quadratic number field and choose an ordering of the Galois group $Gal(F/\mathbb{Q})$, let us say $\{id, \sigma\}$. Then one has an isomorphism

$F \otimes_\mathbb{Q} F \stackrel{\sim}{\longrightarrow} F \oplus F$

sending the elementary tensors $\alpha \otimes \beta$ to $(\alpha\beta, \alpha\sigma(\beta))$.

Can anybody explain me how to construct the preimages of the projectors $(1, 0)$ and $(0, 1)$?

Thanks for your help!

share|cite|improve this question

Hint: Look at the images of $(\sqrt{-d}\otimes \sqrt{-d}) \pm (1 \otimes d)$.

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.