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Results tagged with polynomials
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user 15505
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
7
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1
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Factorization of an irreducible polynomial in the field extension it defines
In field theory, the following fact is used in the construction of splitting fields: Given a field $F$ and an irreducible polynomial $f \in F[x]$, the quotient $F[\alpha]/(f(\alpha))$ is a field exten …
- 2,017
10
votes
If two monic polynomials of $\mathbb{Z}_p[X]$ (p-adic integer coefficient) are relatively pr...
If the two polynomials are $f,g$, then the $\mathbb{Z}_{p}$-module $M := \mathbb{Z}_{p}[X]/(f,g)$ is finitely generated (since at least one of $f,g$ is monic) and satisfies $M \otimes_{\mathbb{Z}_{p}} …
- 2,017