Question

Ideal of $F[X_1,\dotsc,X_n]$ generated by polynomials of bounded degree - small generating subset?

score 41 · Answer 1 · 2023-08-01 13:06:02

41

Views

Ideal of $F[X_1,\dotsc,X_n]$ generated by polynomials of bounded degree - small generating subset?

Published on 01 Aug 2023 - 13:06

score 65 · Answer 2 · 2023-08-11 17:57:43

65

Views

Can quotients by polynomials of different degrees be isomorphic as rings?

Published on 11 Aug 2023 - 17:57

score 52 · Answer 3 · 2023-08-18 12:43:45

52

Views

Number of homomorphisms from $Q[x]/\langle f(x)\rangle$ to $\mathbb{C}$

Published on 18 Aug 2023 - 12:43

score 78 · Answer 4 · 2023-08-28 17:23:54

78

Views

Expressing a multivariate polynomial in terms of its roots

Published on 28 Aug 2023 - 17:23

score 71 · Answer 5 · 2026-03-25 18:47:07

71

Views

Groebner basis over rational vs finite field

Published on 25 Mar 2026 - 18:47

score 34 · Answer 6 · 2023-09-16 00:36:35

34

Views

Can the implication $(x_1 = 0) \rightarrow (p(x_1,...,x_n) = 0)$ be encoded in a system of polynomial constraints in $\mathbb{C}[x_1,...,x_n]$?

Published on 16 Sep 2023 - 0:36

score 84 · Answer 7 · 2023-09-18 17:43:09

84

Views

The Ideal given by the kernel of map $ f \in R \mapsto f(0,0) \in \mathbb C[X,Y]$ is not finitely generated for this particular polynomial subring

Published on 18 Sep 2023 - 17:43

score 66 · Answer 8 · 2026-03-25 13:02:07

66

Views

Is there a name for this sort of ideal?

Published on 25 Mar 2026 - 13:02

score 41 · Answer 9 · 2023-10-05 15:11:46

41

Views

Proof of the formal derivative fraction formula

Published on 05 Oct 2023 - 15:11

score 147 · Answer 10 · 2023-10-09 05:50:13

147

Views

Prove there is a polynomial $d(x) \in \mathbb Q[x]$ that is a gcd of $f(x)$ and $g(x)$ and whose term of minimal degree is $d_rx^r.$ (D&F #9.3.5(a)).

Published on 09 Oct 2023 - 5:50

score 99 · Answer 11 · 2023-10-10 10:27:25

99

Views

The cardinality of the affine algebraic variety $V_{\mathbb{C}}(I)$ and the dimension of $\mathbb{R}[\mathbf{x}]/I$

Published on 10 Oct 2023 - 10:27

score 52 · Answer 12 · 2023-10-17 08:24:41

52

Views

Factorization of $x^{rn} - 1$

Published on 17 Oct 2023 - 8:24

score 34 · Answer 13 · 2023-10-18 19:03:44

34

Views

How to prove that the order of $F[x]/(g(x))$ is $|F|^{\deg(g)}$, where $F$ is a finite field?

Published on 18 Oct 2023 - 19:03

score 19 · Answer 14 · 2023-10-18 19:55:10

19

Views

How do we show $F_2[x]/(x^2 + x) ≅ F_2[x]/(x) × F_2[x]/(x + 1) ≅ F_2 × F_2$?

Published on 18 Oct 2023 - 19:55

score 94 · Answer 15 · 2023-11-01 03:28:05

94

Views

Is $\mathbb Z[x^2]$ an ideal of $\mathbb Z[x]$?

Published on 01 Nov 2023 - 3:28

List Question

Ideal of $F[X_1,\dotsc,X_n]$ generated by polynomials of bounded degree - small generating subset?

Can quotients by polynomials of different degrees be isomorphic as rings?

Number of homomorphisms from $Q[x]/\langle f(x)\rangle$ to $\mathbb{C}$

Expressing a multivariate polynomial in terms of its roots

Groebner basis over rational vs finite field

Can the implication $(x_1 = 0) \rightarrow (p(x_1,...,x_n) = 0)$ be encoded in a system of polynomial constraints in $\mathbb{C}[x_1,...,x_n]$?

The Ideal given by the kernel of map $ f \in R \mapsto f(0,0) \in \mathbb C[X,Y]$ is not finitely generated for this particular polynomial subring

Is there a name for this sort of ideal?

Proof of the formal derivative fraction formula

Prove there is a polynomial $d(x) \in \mathbb Q[x]$ that is a gcd of $f(x)$ and $g(x)$ and whose term of minimal degree is $d_rx^r.$ (D&F #9.3.5(a)).

The cardinality of the affine algebraic variety $V_{\mathbb{C}}(I)$ and the dimension of $\mathbb{R}[\mathbf{x}]/I$

Factorization of $x^{rn} - 1$

How to prove that the order of $F[x]/(g(x))$ is $|F|^{\deg(g)}$, where $F$ is a finite field?

How do we show $F_2[x]/(x^2 + x) ≅ F_2[x]/(x) × F_2[x]/(x + 1) ≅ F_2 × F_2$?

Is $\mathbb Z[x^2]$ an ideal of $\mathbb Z[x]$?

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