Question

Number of roots of a separable polynomial over a connected ring does not exceed deg $f$.

score 52 · Answer 1 · 2019-10-05 16:49:30

52

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Number of roots of a separable polynomial over a connected ring does not exceed deg $f$.

Published on 05 Oct 2019 - 16:49

score 234 · Answer 2 · 2026-03-07 11:07:16

234

Views

Show that $(M_n(R))[X]\cong M_n(R[X])$

Published on 07 Mar 2026 - 11:07

score 376 · Answer 3 · 2019-10-09 02:43:41

376

Views

How to prove this polynomial multiplication is associative and distributes over addition?

Published on 09 Oct 2019 - 2:43

score 803 · Answer 4 · 2026-03-23 00:40:35

803

Views

Subrings of a polynomial ring in one variable

Published on 23 Mar 2026 - 0:40

score 35 · Answer 5 · 2019-10-30 17:12:37

35

Views

An easy question (given as an image) of showing $\ker θ = \langle X^2-1\rangle$ where $ θ : ℝ[X] \to M_2(ℝ)$ is a homomorphism.

Published on 30 Oct 2019 - 17:12

score 53 · Answer 6 · 2019-10-30 17:30:39

53

Views

A question (given as an image) on how to show a polynomial ring is equal to a principal ideal.

Published on 30 Oct 2019 - 17:30

score 258 · Answer 7 · 2019-11-03 03:09:44

258

Views

gcd of $f(x)$ and 0 polynomial

Published on 03 Nov 2019 - 3:09

score 157 · Answer 8 · 2019-11-07 20:09:56

157

Views

Irreducible polynomial in integer polynomial ring with complex root is a reciprocal polynomial

Published on 07 Nov 2019 - 20:09

score 40 · Answer 9 · 2026-03-23 00:35:13

40

Views

basis of tensor products

Published on 23 Mar 2026 - 0:35

score 35 · Answer 10 · 2019-11-12 09:24:00

35

Views

How to use the Division Algorithm (polynomial rings) and evaluation map to prove the Remainder Theorem?

Published on 12 Nov 2019 - 9:24

score 181 · Answer 11 · 2019-11-14 17:31:25

181

Views

Prime ideal in $\mathbb{Z}[X]$ with prime constant polynomials.

Published on 14 Nov 2019 - 17:31

score 33 · Answer 12 · 2019-11-18 16:17:24

33

Views

Algebraic independence of the roots of a biquadratic equation

Published on 18 Nov 2019 - 16:17

score 24 · Answer 13 · 2019-11-19 02:37:09

24

Views

Counting $(0,1)$-polynomials $f \in \mathbb Z/n\mathbb Z[x]$ that are multiples of $x(x+1)\cdots(x + n - 1)$.

Published on 19 Nov 2019 - 2:37

score 317 · Answer 14 · 2019-11-23 02:13:47

317

Views

Monic associates of Polynomials over Integral Domains

Published on 23 Nov 2019 - 2:13

score 148 · Answer 15 · 2019-11-23 10:53:56

148

Views

Module over skew polynomial ring

Published on 23 Nov 2019 - 10:53

List Question

Number of roots of a separable polynomial over a connected ring does not exceed deg $f$.

Show that $(M_n(R))[X]\cong M_n(R[X])$

How to prove this polynomial multiplication is associative and distributes over addition?

Subrings of a polynomial ring in one variable

An easy question (given as an image) of showing $\ker θ = \langle X^2-1\rangle$ where $ θ : ℝ[X] \to M_2(ℝ)$ is a homomorphism.

A question (given as an image) on how to show a polynomial ring is equal to a principal ideal.

gcd of $f(x)$ and 0 polynomial

Irreducible polynomial in integer polynomial ring with complex root is a reciprocal polynomial

basis of tensor products

How to use the Division Algorithm (polynomial rings) and evaluation map to prove the Remainder Theorem?

Prime ideal in $\mathbb{Z}[X]$ with prime constant polynomials.

Algebraic independence of the roots of a biquadratic equation

Counting $(0,1)$-polynomials $f \in \mathbb Z/n\mathbb Z[x]$ that are multiples of $x(x+1)\cdots(x + n - 1)$.

Monic associates of Polynomials over Integral Domains

Module over skew polynomial ring

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