Question

Show that a polynomial is irreducible in $\mathbb { Z } [ i \sqrt { 5 } ]$ but not in $\mathbb { Q } [ i \sqrt { 5 } ]$

score 154 · Answer 1 · 2019-04-04 15:46:28

154

Views

Show that a polynomial is irreducible in $\mathbb { Z } [ i \sqrt { 5 } ]$ but not in $\mathbb { Q } [ i \sqrt { 5 } ]$

Published on 04 Apr 2019 - 15:46

score 1.5k · Answer 2 · 2019-04-04 18:19:12

1.5k

Views

Using Eisenstein criterion show that $x^3+x^2-2x-1$ is irreducible?

Published on 04 Apr 2019 - 18:19

score 417 · Answer 3 · 2019-04-05 00:18:06

417

Views

Irreducible Polynomials In $F_3$

Published on 05 Apr 2019 - 0:18

score 338 · Answer 4 · 2019-04-05 10:09:54

338

Views

Factoring of polynomial over the rationals (quick question)

Published on 05 Apr 2019 - 10:09

score 122 · Answer 5 · 2026-03-25 22:05:34

122

Views

If a monic rational polynomial of degree $p-1$ has $p$-th root of unity as a root, is it the cyclotomic polynomial?

Published on 25 Mar 2026 - 22:05

score 260 · Answer 6 · 2019-04-06 10:29:34

260

Views

Units, Prime Elements and Irreducible elements for polynomials

Published on 06 Apr 2019 - 10:29

score 168 · Answer 7 · 2019-04-06 15:31:35

168

Views

Show that $x^p - m$ is irreducible for prime $p$ and $m \in \mathbb{Q^{\times}}\setminus \left(\mathbb{Q^{\times}}\right)^p$

Published on 06 Apr 2019 - 15:31

score 308 · Answer 8 · 2019-04-06 22:25:46

308

Views

Is $x^4+4x-1$ irreducible in the field $Q[\sqrt{-7}]$?

Published on 06 Apr 2019 - 22:25

score 87 · Answer 9 · 2019-04-07 08:17:22

87

Views

Check the properties of given polynomial of order $7$

Published on 07 Apr 2019 - 8:17

score 50 · Answer 10 · 2026-02-23 03:00:57

50

Views

Degree of $\cos(2\pi/8) + i \sin(2\pi/8)$ over $\mathbb{Q}$

Published on 23 Feb 2026 - 3:00

score 691 · Answer 11 · 2026-03-25 11:06:38

691

Views

Degree of splitting field of $X^4+2X^2+2$ over $\mathbf{Q}$

Published on 25 Mar 2026 - 11:06

score 54 · Answer 12 · 2026-03-26 16:26:33

54

Views

Units, Primes and Irreducibles

Published on 26 Mar 2026 - 16:26

score 54 · Answer 13 · 2019-04-11 02:55:26

54

Views

$f(x) = x$ in $(\mathbb{Z}/6\mathbb{Z})[x]$ factors as $(3x+4)(4x+3)$

Published on 11 Apr 2019 - 2:55

score 132 · Answer 14 · 2026-03-25 09:28:29

132

Views

Is this proof of a irreducibility criterion in an integral domain correct?

Published on 25 Mar 2026 - 9:28

score 1.2k · Answer 15 · 2019-04-17 17:23:45

1.2k

Views

Is $x^3-1$ reducible over $\mathbb{Q}$

Published on 17 Apr 2019 - 17:23

List Question

Show that a polynomial is irreducible in $\mathbb { Z } [ i \sqrt { 5 } ]$ but not in $\mathbb { Q } [ i \sqrt { 5 } ]$

Using Eisenstein criterion show that $x^3+x^2-2x-1$ is irreducible?

Irreducible Polynomials In $F_3$

Factoring of polynomial over the rationals (quick question)

If a monic rational polynomial of degree $p-1$ has $p$-th root of unity as a root, is it the cyclotomic polynomial?

Units, Prime Elements and Irreducible elements for polynomials

Show that $x^p - m$ is irreducible for prime $p$ and $m \in \mathbb{Q^{\times}}\setminus \left(\mathbb{Q^{\times}}\right)^p$

Is $x^4+4x-1$ irreducible in the field $Q[\sqrt{-7}]$?

Check the properties of given polynomial of order $7$

Degree of $\cos(2\pi/8) + i \sin(2\pi/8)$ over $\mathbb{Q}$

Degree of splitting field of $X^4+2X^2+2$ over $\mathbf{Q}$

Units, Primes and Irreducibles

$f(x) = x$ in $(\mathbb{Z}/6\mathbb{Z})[x]$ factors as $(3x+4)(4x+3)$

Is this proof of a irreducibility criterion in an integral domain correct?

Is $x^3-1$ reducible over $\mathbb{Q}$

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