Question

Isomorphism between quotient spaces adjoining elements

score 145 · Answer 1 · 2026-03-26 22:50:37

145

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Isomorphism between quotient spaces adjoining elements

Published on 26 Mar 2026 - 22:50

score 32 · Answer 2 · 2026-03-27 03:59:50

32

Views

Prove the following Lemma in the polynomial rings.

Published on 27 Mar 2026 - 3:59

score 325 · Answer 3 · 2020-11-04 22:48:28

325

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Show that $I=\langle x+1, x^2+1\rangle$ is maximal in $\mathbb Z[x]$.

Published on 04 Nov 2020 - 22:48

score 44 · Answer 4 · 2020-11-04 23:57:13

44

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Let $\Bbb R$ be a field of all real numbers. Prove that $x+1$ is not a unit in $\Bbb R[x]$.

Published on 04 Nov 2020 - 23:57

score 83 · Answer 5 · 2026-03-27 03:58:07

83

Views

Show that $\phi:\mathbb{Q}(\sqrt{3}) \rightarrow M_{2}(\mathbb{Q})$ maps identity to identity.

Published on 27 Mar 2026 - 3:58

score 157 · Answer 6 · 2020-11-05 10:06:25

157

Views

Find gcd of $a = 170 + 32\sqrt{3}$ and $b = 61 + 35\sqrt{3}.$ Then find $f,g \in \mathbb{Z}[\sqrt{3}]$ such that $af + bg = d$ using norm function.

Published on 05 Nov 2020 - 10:06

score 34 · Answer 7 · 2020-11-05 21:07:31

34

Views

Lacking some steps in a proof regarding set of units of $\mathbb{Z}[\sqrt{3}].$

Published on 05 Nov 2020 - 21:07

score 72 · Answer 8 · 2026-02-23 08:26:48

72

Views

Show that $\mathbb{Z}[\sqrt{3}]$ satisfies the following division property:

Published on 23 Feb 2026 - 8:26

score 124 · Answer 9 · 2020-11-06 02:57:53

124

Views

Show that $\mathbb{Z}[\sqrt{3}]$ is dense in $\mathbb{R}.$

Published on 06 Nov 2020 - 2:57

score 99 · Answer 10 · 2020-11-10 10:54:35

99

Views

Show that the ring $\Bbb C[x,y,z]/\langle 2x^2y-5xy^3+z\rangle $ is a UFD

Published on 10 Nov 2020 - 10:54

score 116 · Answer 11 · 2020-11-12 16:54:59

116

Views

Is the extension of a prime ideal over a polynomial ring over a field still prime?

Published on 12 Nov 2020 - 16:54

score 95 · Answer 12 · 2020-11-14 19:59:10

95

Views

Why for some $r_{i} \in R$ and not for some $r_{i} \in R[X]$?

Published on 14 Nov 2020 - 19:59

score 49 · Answer 13 · 2020-11-15 18:22:18

49

Views

Why we need to differentiate between the deg. of the polynomial being stationary and the leading coefficient being stationary?

Published on 15 Nov 2020 - 18:22

score 248 · Answer 14 · 2020-11-19 10:16:32

248

Views

Show that $Z^2 + Y^3 + X^5$ is irreducible in $\mathbb C[X,Y,Z].$

Published on 19 Nov 2020 - 10:16

score 128 · Answer 15 · 2020-11-28 15:54:42

128

Views

ideals in the ring $\frac{F[x]}{(p(x))}$

Published on 28 Nov 2020 - 15:54

List Question

Isomorphism between quotient spaces adjoining elements

Prove the following Lemma in the polynomial rings.

Show that $I=\langle x+1, x^2+1\rangle$ is maximal in $\mathbb Z[x]$.

Let $\Bbb R$ be a field of all real numbers. Prove that $x+1$ is not a unit in $\Bbb R[x]$.

Show that $\phi:\mathbb{Q}(\sqrt{3}) \rightarrow M_{2}(\mathbb{Q})$ maps identity to identity.

Find gcd of $a = 170 + 32\sqrt{3}$ and $b = 61 + 35\sqrt{3}.$ Then find $f,g \in \mathbb{Z}[\sqrt{3}]$ such that $af + bg = d$ using norm function.

Lacking some steps in a proof regarding set of units of $\mathbb{Z}[\sqrt{3}].$

Show that $\mathbb{Z}[\sqrt{3}]$ satisfies the following division property:

Show that $\mathbb{Z}[\sqrt{3}]$ is dense in $\mathbb{R}.$

Show that the ring $\Bbb C[x,y,z]/\langle 2x^2y-5xy^3+z\rangle $ is a UFD

Is the extension of a prime ideal over a polynomial ring over a field still prime?

Why for some $r_{i} \in R$ and not for some $r_{i} \in R[X]$?

Why we need to differentiate between the deg. of the polynomial being stationary and the leading coefficient being stationary?

Show that $Z^2 + Y^3 + X^5$ is irreducible in $\mathbb C[X,Y,Z].$

ideals in the ring $\frac{F[x]}{(p(x))}$

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