Question

Difference in $\operatorname{Spec}(R[X])$ and $\operatorname{Spec}(F[X])$ when $R$ is a ring v/s $F$ is a field?

score 75 · Answer 1 · 2020-02-26 11:58:22

75

Views

Difference in $\operatorname{Spec}(R[X])$ and $\operatorname{Spec}(F[X])$ when $R$ is a ring v/s $F$ is a field?

Published on 26 Feb 2020 - 11:58

score 74 · Answer 2 · 2026-03-25 07:44:05

74

Views

Divisibility of a general polynomial of a rational expression

Published on 25 Mar 2026 - 7:44

score 425 · Answer 3 · 2020-03-24 18:38:53

425

Views

Torsion in finitely generated modules over polynomial rings

Published on 24 Mar 2020 - 18:38

score 48 · Answer 4 · 2020-03-25 04:20:43

48

Views

Existence of a polynomial in $C[x,y]$

Published on 25 Mar 2020 - 4:20

score 171 · Answer 5 · 2020-04-04 20:30:15

171

Views

Prove $\{a(c):a(x) \in F[x]\}$ is an integral domain isomorphic to $F[x]$

Published on 04 Apr 2020 - 20:30

score 252 · Answer 6 · 2020-04-05 19:03:07

252

Views

Is it true that the units in $\mathbb{Q}[x,y]$ are precisely the constant polynomials?

Published on 05 Apr 2020 - 19:03

score 7.5k · Answer 7 · 2026-03-24 21:12:22

7.5k

Views

Gauss's Lemma Proof

Published on 24 Mar 2026 - 21:12

score 31 · Answer 8 · 2020-04-25 00:17:44

31

Views

Factoring an ideal in a quotient polynomial ring

Published on 25 Apr 2020 - 0:17

score 94 · Answer 9 · 2020-05-04 10:03:54

94

Views

Proof of sub field and polynomial ring

Published on 04 May 2020 - 10:03

score 1.9k · Answer 10 · 2020-05-06 04:04:14

1.9k

Views

Prove that the principal ideal generated by $x$ in the polynomial ring $R[x]$ is a prime ideal iff $R$ is an integral domain.

Published on 06 May 2020 - 4:04

score 110 · Answer 11 · 2026-03-22 06:14:13

110

Views

Finding the length of the kernel of a map in Macaulay2

Published on 22 Mar 2026 - 6:14

score 133 · Answer 12 · 2026-03-25 03:20:42

133

Views

Ideals in $R$ and $R[x]$

Published on 25 Mar 2026 - 3:20

score 35 · Answer 13 · 2020-06-01 13:52:34

35

Views

How to prove that $(\Bbb{Z}[t]+t\Bbb{R}[t])/t\Bbb{R}[t]\cong\Bbb{Z}\cong\Bbb{Z}[t]/t\Bbb{Z}[t]\cong\Bbb{Z}[t]/(\Bbb{Z}[t]\cap t\Bbb{R}[t])$?

Published on 01 Jun 2020 - 13:52

score 44 · Answer 14 · 2020-06-01 16:50:31

44

Views

For which ideal $I$ of $\Bbb Z[t]$ is $\mathbb{Z}[t]/I\cong\Bbb Z_{11}$?

Published on 01 Jun 2020 - 16:50

score 92 · Answer 15 · 2020-06-04 21:38:55

92

Views

Under which conditions the rings $\mathbb{Z}_p[x]/(x^n+1)$ and $\mathbb{Z}_p[x]/(x^n-1)$ are fields? (for $p$ prime)

Published on 04 Jun 2020 - 21:38

List Question

Difference in $\operatorname{Spec}(R[X])$ and $\operatorname{Spec}(F[X])$ when $R$ is a ring v/s $F$ is a field?

Divisibility of a general polynomial of a rational expression

Torsion in finitely generated modules over polynomial rings

Existence of a polynomial in $C[x,y]$

Prove $\{a(c):a(x) \in F[x]\}$ is an integral domain isomorphic to $F[x]$

Is it true that the units in $\mathbb{Q}[x,y]$ are precisely the constant polynomials?

Gauss's Lemma Proof

Factoring an ideal in a quotient polynomial ring

Proof of sub field and polynomial ring

Prove that the principal ideal generated by $x$ in the polynomial ring $R[x]$ is a prime ideal iff $R$ is an integral domain.

Finding the length of the kernel of a map in Macaulay2

Ideals in $R$ and $R[x]$

How to prove that $(\Bbb{Z}[t]+t\Bbb{R}[t])/t\Bbb{R}[t]\cong\Bbb{Z}\cong\Bbb{Z}[t]/t\Bbb{Z}[t]\cong\Bbb{Z}[t]/(\Bbb{Z}[t]\cap t\Bbb{R}[t])$?

For which ideal $I$ of $\Bbb Z[t]$ is $\mathbb{Z}[t]/I\cong\Bbb Z_{11}$?

Under which conditions the rings $\mathbb{Z}_p[x]/(x^n+1)$ and $\mathbb{Z}_p[x]/(x^n-1)$ are fields? (for $p$ prime)

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