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 Apr 24 awarded Popular Question Apr 7 awarded Good Question Apr 2 awarded Popular Question Feb 1 answered How do we conclude that $f(x)=0, \forall x\in \mathbb{R}$ ? Dec 18 answered How to show that $Sp\{u+v-3w,2v-w,t+w,v+w\} = Sp\{u,v,w,t\}$ Dec 16 awarded Yearling Nov 18 awarded Popular Question Nov 9 accepted Proving that the maximal abelian extension contains all abelian extensions Nov 9 answered Prove the infinite union is not regular Nov 7 comment An exercise related to Krull topology - showing that two bases define the same topology @random123 - Could please you add some details ? Nov 7 asked An exercise related to Krull topology - showing that two bases define the same topology Nov 6 accepted What is a good theoretical, yet somewhat practical, book about error correction codes? Nov 6 accepted Subgroups of Index $2$ of $(\mathbb{Z}_{2})^{\aleph_{0}}$ Nov 6 comment Subgroups of Index $2$ of $(\mathbb{Z}_{2})^{\aleph_{0}}$ @AsafKaragila - I mean the one group, up to isomorphism, of order $2$. I don't know about the dyadic integers (yet ?) Nov 6 revised Subgroups of Index $2$ of $(\mathbb{Z}_{2})^{\aleph_{0}}$ added 104 characters in body Nov 6 asked Subgroups of Index $2$ of $(\mathbb{Z}_{2})^{\aleph_{0}}$ Nov 6 answered Prove that the Language $L= \{ 0^n1^m \;|\; n,m \ge 0 \}$ is regular Nov 3 awarded Enlightened Nov 3 awarded Nice Answer Nov 2 comment Checking irreducibility of a polynomial in $\mathbb{K}[x,y]$ and PAC fields Thank you for posting an answer, I think there is a counter example for your claim: Take $K=\mathbb{R}$ and $\phi=-x^{2}$ which is separable as every irreducible factor is separable. $n=2$ and the $n$-th roots of unity are $\pm1\in\mathbb{R}$. $F(x,y)=y^{2}-\phi(x)=y^{2}+x^{2}=(y+ix)(y-ix)$ is a factorization over $\mathbb{C}$ so that $F(x,y)$ is not irreducible as claimed. Did I miss something ?