Question

Is R[x] a ring of functions or a ring of expressions?

score 506 · Answer 1 · 2019-11-24 19:48:11

506

Views

Is R[x] a ring of functions or a ring of expressions?

Published on 24 Nov 2019 - 19:48

score 57 · Answer 2 · 2026-03-25 11:12:16

57

Views

Finding a polynomial ring embedded in a fg algebra over complex numbers

Published on 25 Mar 2026 - 11:12

score 69 · Answer 3 · 2019-12-02 16:53:31

69

Views

Why is \begin{align}2x^2+2x=2x-2 | F_3[x] / (x^2 +1)? \end{align}

Published on 02 Dec 2019 - 16:53

score 278 · Answer 4 · 2019-12-02 20:51:20

278

Views

Krull dimension of polynomial ring in countably many variables

Published on 02 Dec 2019 - 20:51

score 187 · Answer 5 · 2019-12-05 19:10:48

187

Views

Does the existence of a common solution to a set of polynomials over a field extension imply a common solution over the subfield

Published on 05 Dec 2019 - 19:10

score 374 · Answer 6 · 2019-12-09 01:38:30

374

Views

Relationship between a solution in $\mathbb{C}$ to a finite set of polynomials over $\mathbb{Z}$ and solutions in finite fields

Published on 09 Dec 2019 - 1:38

score 193 · Answer 7 · 2019-12-09 05:02:22

193

Views

Another proof for complex solutions and solutions in finite fields

Published on 09 Dec 2019 - 5:02

score 219 · Answer 8 · 2019-12-14 14:30:14

219

Views

Prime ideal in ring of polynomials

Published on 14 Dec 2019 - 14:30

score 87 · Answer 9 · 2026-03-25 06:58:56

87

Views

Show that if $f \sim^{\mathcal{R}} g$, then $\text{ord } (f) = \text{ord } (g)$.

Published on 25 Mar 2026 - 6:58

score 47 · Answer 10 · 2026-03-23 00:31:02

47

Views

polynomial multiplication with integer polynomial result

Published on 23 Mar 2026 - 0:31

score 69 · Answer 11 · 2020-01-08 00:13:14

69

Views

Nontrivial homomorphism between $\mathbb{Q}[x]/(x^3-1)$ and $\mathbb{Q}[x]/(x^2+x+1)$

Published on 08 Jan 2020 - 0:13

score 1.5k · Answer 12 · 2020-01-10 22:21:15

1.5k

Views

Show $\mathbb Z[x]/(x^2-cx) \ncong \mathbb Z \times \mathbb Z$.

Published on 10 Jan 2020 - 22:21

score 104 · Answer 13 · 2020-01-23 14:41:05

104

Views

Redundancy Hungerford: Ex. 4.1.13 & 4.1.15, zero divisors and units

Published on 23 Jan 2020 - 14:41

score 36 · Answer 14 · 2020-02-02 18:34:47

36

Views

Polynomials in polynomial ring

Published on 02 Feb 2020 - 18:34

score 90 · Answer 15 · 2020-02-18 16:39:11

90

Views

Eisenbud 1.21a $G(n):= F(n)-F(n-1)$, given $G(n)$ is integer-valued, then so is $F(n)$.

Published on 18 Feb 2020 - 16:39

List Question

Is R[x] a ring of functions or a ring of expressions?

Finding a polynomial ring embedded in a fg algebra over complex numbers

Why is \begin{align}2x^2+2x=2x-2 | F_3[x] / (x^2 +1)? \end{align}

Krull dimension of polynomial ring in countably many variables

Does the existence of a common solution to a set of polynomials over a field extension imply a common solution over the subfield

Relationship between a solution in $\mathbb{C}$ to a finite set of polynomials over $\mathbb{Z}$ and solutions in finite fields

Another proof for complex solutions and solutions in finite fields

Prime ideal in ring of polynomials

Show that if $f \sim^{\mathcal{R}} g$, then $\text{ord } (f) = \text{ord } (g)$.

polynomial multiplication with integer polynomial result

Nontrivial homomorphism between $\mathbb{Q}[x]/(x^3-1)$ and $\mathbb{Q}[x]/(x^2+x+1)$

Show $\mathbb Z[x]/(x^2-cx) \ncong \mathbb Z \times \mathbb Z$.

Redundancy Hungerford: Ex. 4.1.13 & 4.1.15, zero divisors and units

Polynomials in polynomial ring

Eisenbud 1.21a $G(n):= F(n)-F(n-1)$, given $G(n)$ is integer-valued, then so is $F(n)$.

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