query: I have to show no proper intermediate fields exist between $Z_2$ and $GF(2^3)$
positive_passages.docid: 6855
positive_passages.text: Subfields of finite fields
negative_passages.docid: 104851
negative_passages.text: A finite field cannot be an ordered field.
negative_passages.docid: 140808
negative_passages.text: Problem on Galois theory and irreducible polynomial
negative_passages.docid: 46648
negative_passages.text: How to prove the existence of a splitting field?
negative_passages.docid: 17991
negative_passages.text: Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
negative_passages.docid: 135606
negative_passages.text: No function $f:\mathbb{Z}\rightarrow \{1, 2, 3\}$ satisfying $f(x)\ne f(y)$ for all integers $x,y$ and $|x-y|\in\{2, 3, 5\}$
negative_passages.docid: 135524
negative_passages.text: Is $\mathrm{ZFC}^E$ outright inconsistent?
negative_passages.docid: 124864
negative_passages.text: A not free $\mathbb{Z}$-module
negative_passages.docid: 26764
negative_passages.text: Proving that $\mathbb R^3$ cannot be made into a real division algebra (and that extending complex multiplication would not work)
negative_passages.docid: 7010
negative_passages.text: Example of two non-isomorphic fields which embed inside each other
negative_passages.docid: 88474
negative_passages.text: $\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
negative_passages.docid: 120940
negative_passages.text: An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
negative_passages.docid: 148192
negative_passages.text: In a field that is the direct product of two fields, why isn't it a field?
negative_passages.docid: 3711
negative_passages.text: Finding the intermediate fields of $\Bbb{Q}(\zeta_7)$.
negative_passages.docid: 67157
negative_passages.text: Example of an non-normal inseparable field extension
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: 27021
negative_passages.text: Show that $Q[\sqrt3]$ is a field