query: Dummit exercise 14.3.11: extension degree of finite fields
positive_passages.docid: 54192
positive_passages.text: Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
negative_passages.docid: 46795
negative_passages.text: Explicit construction of a finite field with $p^n$ elements
negative_passages.docid: 14270
negative_passages.text: Polynomial divisibility is unchanged by coeff. field extension
negative_passages.docid: 31142
negative_passages.text: Why does $K \leadsto K(X)$ preserve the degree of field extensions?
negative_passages.docid: 95692
negative_passages.text: Factoring polynomials of the form $1+x+\cdots +x^{p-1}$ in finite field
negative_passages.docid: 46572
negative_passages.text: Degree of a splitting field is no greater than $n!$
negative_passages.docid: 14918
negative_passages.text: Degree of splitting field of $X^n-1$ over some finite field
negative_passages.docid: 114519
negative_passages.text: An elementary question regarding a multiplicative character over finite fields
negative_passages.docid: 40502
negative_passages.text: The Degree of Zero Polynomial.
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: 75946
negative_passages.text: Determine the degree of the extension $\mathbb{Q}(\sqrt{3 + 2\sqrt{2}})$.
negative_passages.docid: 106737
negative_passages.text: A problem on field extension
negative_passages.docid: 92677
negative_passages.text: Infinite algebraic extension of a finite field
negative_passages.docid: 129476
negative_passages.text: The trace map in a finite field.
negative_passages.docid: 147982
negative_passages.text: Exercise 1.10 from Silverman "The Arithmetic of Elliptic Curves "
negative_passages.docid: 68753
negative_passages.text: Elements in finite field extensions
negative_passages.docid: 80538
negative_passages.text: Fields extensions over isomorphic fields of different degrees