What's the name of this set

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

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

As an example $S(\mathbb{R}) = \\{-1, 1\\}$, $S(\mathbb{C}) = \\{1\\}$, $S(\mathbb{Z}_3) = \\{1, 2\\}$, $S(\mathbb{Z}_5) = \\{1, 2\\}$. Certainly collections are not one-of-a-kind like $S(\mathbb{R}) = \\{-e,\pi\\}$ is additionally feasible.

(Sorry if I abuse terms - I have not located english translation - yet I located it valuable to generalise the trademark of square polynomials ).

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2019-05-07 14:59:18
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Answers: 1

If I am decoding your symbols appropriately, I would certainly call $S$ "a set of coset reps for $K^{\times}/(K^{\times})^2$."

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2019-05-09 10:56:17
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