Question

Prove that an integer monic polynomial with nonzero constant term and exactly one root outside the open unit disk is irreducible over $\mathbb{Q}$

score 546 · Answer 1 · 2017-06-03 12:35:47

546

Views

Prove that an integer monic polynomial with nonzero constant term and exactly one root outside the open unit disk is irreducible over $\mathbb{Q}$

Published on 03 Jun 2017 - 12:35

score 96 · Answer 2 · 2017-06-04 13:35:37

96

Views

Irreducibility of a family of quintic polynomials with solvable Galois group order 20

Published on 04 Jun 2017 - 13:35

score 900 · Answer 3 · 2017-06-06 17:24:38

900

Views

Show that $f(x)=x^2+x+4$ is irreducible over $\mathbb{Z}_{11}$

Published on 06 Jun 2017 - 17:24

score 194 · Answer 4 · 2026-03-30 00:17:55

194

Views

prime and irreducible elements $\equiv 1$ modulo $4$

Published on 30 Mar 2026 - 0:17

score 160 · Answer 5 · 2017-06-10 09:49:36

160

Views

Using Jordan's theorem to find Galois group for a polynomial

Published on 10 Jun 2017 - 9:49

score 920 · Answer 6 · 2017-06-10 15:13:13

920

Views

About isomorphisms, minimal polynomials and roots

Published on 10 Jun 2017 - 15:13

score 49 · Answer 7 · 2017-06-11 16:52:10

49

Views

Trying to find the mistake

Published on 11 Jun 2017 - 16:52

score 479 · Answer 8 · 2026-03-28 10:04:22

479

Views

Is it true that an ideal is prime iff the reduced Gröbner basis contains irreducible polynomials

Published on 28 Mar 2026 - 10:04

score 55 · Answer 9 · 2017-06-13 17:28:36

55

Views

Irreducibility of $X^4 + a^2$ with odd $a$

Published on 13 Jun 2017 - 17:28

score 1.1k · Answer 10 · 2017-06-15 04:21:20

1.1k

Views

Let $F,K$ be fields, prove that any element in $K$ that is not in $F$ is irreducible in $F[x]$ of degree $p$.

Published on 15 Jun 2017 - 4:21

score 83 · Answer 11 · 2026-03-28 20:41:22

83

Views

Find $(x + 1)^{−3}$ in $\mathbb{Z}_2[x]/(x^5 + x^4 + 1)$

Published on 28 Mar 2026 - 20:41

score 319 · Answer 12 · 2017-06-16 12:39:37

319

Views

Show that polynomial is reducible over $\mathbb{Q}[X]$.

Published on 16 Jun 2017 - 12:39

score 927 · Answer 13 · 2017-06-16 22:44:44

927

Views

An irreducible polynomial of degree 8 over a field $\mathbb{F}_p$

Published on 16 Jun 2017 - 22:44

score 1k · Answer 14 · 2017-06-20 01:13:32

1k

Views

Criteria for a prime degree field extension to be Galois

Published on 20 Jun 2017 - 1:13

score 1.8k · Answer 15 · 2017-06-20 07:36:27

1.8k

Views

Irreducible polynomial over integers : sufficient conditions?

Published on 20 Jun 2017 - 7:36

List Question

Prove that an integer monic polynomial with nonzero constant term and exactly one root outside the open unit disk is irreducible over $\mathbb{Q}$

Irreducibility of a family of quintic polynomials with solvable Galois group order 20

Show that $f(x)=x^2+x+4$ is irreducible over $\mathbb{Z}_{11}$

prime and irreducible elements $\equiv 1$ modulo $4$

Using Jordan's theorem to find Galois group for a polynomial

About isomorphisms, minimal polynomials and roots

Trying to find the mistake

Is it true that an ideal is prime iff the reduced Gröbner basis contains irreducible polynomials

Irreducibility of $X^4 + a^2$ with odd $a$

Let $F,K$ be fields, prove that any element in $K$ that is not in $F$ is irreducible in $F[x]$ of degree $p$.

Find $(x + 1)^{−3}$ in $\mathbb{Z}_2[x]/(x^5 + x^4 + 1)$

Show that polynomial is reducible over $\mathbb{Q}[X]$.

An irreducible polynomial of degree 8 over a field $\mathbb{F}_p$

Criteria for a prime degree field extension to be Galois

Irreducible polynomial over integers : sufficient conditions?

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