Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

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's take field $(K, +,\times,0,1)$. Let's take set $S(K) \subset K$ such that:

\[ \forall~e \in K,\exists~a \in S(K),\exists~p \in K: e = a \times p \times p \] \[ \lnot \exists~a, b \in S(K), \exists~p \in K, (a \times p \times p = b \land a \neq b) \]

For example $S(\mathbb{R}) = \\{-1, 1\\}$, $S(\mathbb{C}) = \\{1\\}$, $S(\mathbb{Z}_3) = \\{1, 2\\}$, $S(\mathbb{Z}_5) = \\{1, 2\\}$. Of course sets are not unique like $S(\mathbb{R}) = \\{-e,\pi\\}$ is also possible.

(Sorry if I misuse terms - I haven't found english translation - but I found it useful to generalize the signature of quadratic polynomials).

share|cite|improve this question
up vote 2 down vote accepted

If I am deciphering your notation correctly, I would call $S$ "a set of coset representatives for $K^{\times}/(K^{\times})^2$."

share|cite|improve this answer
I haven't check it fully but from what I understend it looks like this. – Maciej Piechotka Aug 9 '10 at 20:28

Your Answer


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.