query: Determine whether the extension is Galois
positive_passages.docid: 12524
positive_passages.text: Galois group of $x^3 - 2 $ over $\mathbb Q$
negative_passages.docid: 18048
negative_passages.text: Easy criteria to determine isomorphism of fields?
negative_passages.docid: 10942
negative_passages.text: How to check if a glob has an expansion?
negative_passages.docid: 80295
negative_passages.text: Field extensions and algebraic/transcendental elements
negative_passages.docid: 19525
negative_passages.text: Showing field extension $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})/\mathbb{Q}$ degree 8
negative_passages.docid: 120943
negative_passages.text: Galois field extension and number of intermediate fields
negative_passages.docid: 622
negative_passages.text: Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$
negative_passages.docid: 73713
negative_passages.text: Prove that $\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})})$ is Galois over $\mathbb{Q}$ is Galois and determine the Galois group
negative_passages.docid: 9422
negative_passages.text: Computing the Galois group of polynomials $x^n-a \in \mathbb{Q}[x]$
negative_passages.docid: 56551
negative_passages.text: Multiplicative group of field extension over base field
negative_passages.docid: 19511
negative_passages.text: Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
negative_passages.docid: 106737
negative_passages.text: A problem on field extension
negative_passages.docid: 7567
negative_passages.text: Degree of Field Extensions and $F(\alpha)$
negative_passages.docid: 107694
negative_passages.text: How to test if a number is a primitive root?
negative_passages.docid: 39755
negative_passages.text: In a faithfully flat ring extension, is $\operatorname{ht}I=\operatorname{ht}IS$ right?
negative_passages.docid: 127796
negative_passages.text: Degree of field extension $F(x) / F(x^2 + 1 / x^2)$
negative_passages.docid: 48093
negative_passages.text: Irreducible polynomial in field extension