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15
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Show $x^{p}+a$ is reducible in $\mathbb{Z}_p[x]$

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#abstract-algebra #irreducible-polynomials
740
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Polynomial with rational coefficients

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#abstract-algebra #polynomials #irreducible-polynomials #rational-numbers #minimal-polynomials
420
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In the polynomial ring over an integral domain, monomials decompose into monomials.

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#abstract-algebra #irreducible-polynomials
846
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Generalized Eisenstein's Criterion over Integral Domains?

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#abstract-algebra #polynomials #irreducible-polynomials
74
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Understanding the inductive proof about field extension in Artin

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#abstract-algebra #polynomials #field-theory #irreducible-polynomials
432
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Showing that $x^{14}+8x^{13}+3$ is irreducible in $ℚ[x]$ (need further explanation on the solution)

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#abstract-algebra #polynomials #field-theory #finite-fields #irreducible-polynomials
427
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Show that $\mathbb{Q}[\sqrt{2}]$ is a field

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#abstract-algebra #ring-theory #field-theory #irreducible-polynomials #principal-ideal-domains
3.2k
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Irreducibility of polynomials in two variables

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#abstract-algebra #polynomials #irreducible-polynomials
37
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Factorizing polynomials to irreducibility only

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#field-theory #factoring #irreducible-polynomials
281
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Quadratic Cyclotomic Polynomials

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#irreducible-polynomials #cyclotomic-polynomials
294
Views

Quadratic Cyclotomic Polynomials

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#irreducible-polynomials #cyclotomic-polynomials
174
Views

Irreducible Quadratic Cyclomatic Polynomial

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#irreducible-polynomials #cyclotomic-polynomials
444
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Irreducible Quadratic Cyclotomic Polynomial

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#irreducible-polynomials #cyclotomic-polynomials
1.3k
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Irreducible polynomial in field extension

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#polynomials #field-theory #extension-field #irreducible-polynomials
822
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Factorize $x^9 - 1 $ in $\mathbb F_3[x]$

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#abstract-algebra #polynomials #irreducible-polynomials

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