query: How does greatest common divisor effected by field extension
positive_passages.docid: 25891
positive_passages.text: GCD in polynomial rings with coefficients in a field extension
negative_passages.docid: 106737
negative_passages.text: A problem on field extension
negative_passages.docid: 146446
negative_passages.text: Infinite Degree Algebraic Field Extensions
negative_passages.docid: 139861
negative_passages.text: Support of a module with extended scalars
negative_passages.docid: 78350
negative_passages.text: When does a finite ring become a finite field?
negative_passages.docid: 78222
negative_passages.text: Can any monomorphism of a subfield of a splitting field be extended to an automorphism?
negative_passages.docid: 113216
negative_passages.text: No field properly between $\mathbb Q$ and $E$ iff $G(K/\mathbb Q) \cong A_4$ or $S_4$
negative_passages.docid: 143219
negative_passages.text: If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$
negative_passages.docid: 36862
negative_passages.text: A question about proving that there is no greatest common divisor
negative_passages.docid: 26999
negative_passages.text: How is the degree of the minimal polynomial related to the degree of a field extension?
negative_passages.docid: 27250
negative_passages.text: Greatest common divisor of two relatively primes
negative_passages.docid: 151978
negative_passages.text: Splitting field of x^3-2 as a simple extension
negative_passages.docid: 69935
negative_passages.text: Field extensions of finite degree and primitive elements
negative_passages.docid: 56420
negative_passages.text: Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$
negative_passages.docid: 155642
negative_passages.text: Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
negative_passages.docid: 127796
negative_passages.text: Degree of field extension $F(x) / F(x^2 + 1 / x^2)$
negative_passages.docid: 25793
negative_passages.text: Extension fields isomorphic to fields of matrices