query: Galois Theory Quadratic Subfield
positive_passages.docid: 22158
positive_passages.text: Find the quadratic sub field of $\mathbb Q(\zeta_7)$ which can be expressed in the form $\mathbb Q(\sqrt D)$,where $D$ is an integer.
negative_passages.docid: 8602
negative_passages.text: Galois Group of $(x^2-p_1)\cdots(x^2-p_n)$
negative_passages.docid: 72478
negative_passages.text: What is the isomorphism between the fields $(Z_2[x]^{<3},+_{x^3+x^2+1},\times_{x^3+x^2+1})$ and $(Z_2[x]^{<3},+_{x^3+x+1},\times_{x^3+x+1})$?
negative_passages.docid: 45627
negative_passages.text: Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$
negative_passages.docid: 49150
negative_passages.text: Subscript R notation for the finite fields
negative_passages.docid: 100439
negative_passages.text: Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$
negative_passages.docid: 80538
negative_passages.text: Fields extensions over isomorphic fields of different degrees
negative_passages.docid: 98577
negative_passages.text: Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
negative_passages.docid: 82576
negative_passages.text: Intersection of two subfields of the Rational Function Field in characteristic $0$
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: 50785
negative_passages.text: Galois group of $x^4-5$
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: 59108
negative_passages.text: Book for field and galois theory.
negative_passages.docid: 103654
negative_passages.text: A finite field extension that is not simple
negative_passages.docid: 158588
negative_passages.text: Determine the Galois group of the polynomial $(x^3-2)(x^3-3)(x^2-2)$ over $\mathbb{Q}(\sqrt {-3})$
negative_passages.docid: 56647
negative_passages.text: Structure of $Gal(\mathbb{Q}(\zeta_{15})/\mathbb{Q})$?
negative_passages.docid: 81844
negative_passages.text: How would you show that field automorphisms fix prime subfields?