Question

Show that if $R$ is an integral domain, then $R[x]$ is an integral domain

score 656 · Answer 1 · 2026-03-25 01:18:18

656

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Show that if $R$ is an integral domain, then $R[x]$ is an integral domain

Published on 25 Mar 2026 - 1:18

score 3.9k · Answer 2 · 2018-05-02 14:08:39

3.9k

Views

Proof verification: There exists a positive real number $x$ such that $x^2=2$

Published on 02 May 2018 - 14:08

score 68 · Answer 3 · 2026-03-25 16:20:40

68

Views

Step by step explaintions needed for integral problems

Published on 25 Mar 2026 - 16:20

score 3.5k · Answer 4 · 2026-03-28 16:58:02

3.5k

Views

Assume that the ring $R$ has a commutative multiplication. Prove that the set of nilpotent elements $N$ forms a subring of $R$

Published on 28 Mar 2026 - 16:58

score 88 · Answer 5 · 2018-05-02 20:33:26

88

Views

Result comparison of a trigonometric equation

Published on 02 May 2018 - 20:33

score 2.1k · Answer 6 · 2018-05-02 21:27:45

2.1k

Views

Proof verification: Diffeomorphism is an isometry if and only if it preserves the arclength of a parametrised curve.

Published on 02 May 2018 - 21:27

score 50 · Answer 7 · 2026-03-24 22:12:58

50

Views

Necessity of data smoothness for abstract parabolic IVP

Published on 24 Mar 2026 - 22:12

score 7.3k · Answer 8 · 2018-05-03 11:22:40

7.3k

Views

How can one prove that $\sqrt{ 2} \cdot \sqrt{ 3} = \sqrt{ 6}$?

Published on 03 May 2018 - 11:22

score 57 · Answer 9 · 2018-05-03 11:45:14

57

Views

Proof check in Linear Algebra with Diagonalizable operator

Published on 03 May 2018 - 11:45

score 174 · Answer 10 · 2026-03-26 06:30:59

174

Views

Fourier transform identity. $\int\limits_{-\infty}^{\infty}\hat f(x)g(x)\,dx=\int\limits_{-\infty}^{\infty} f(x)\hat g(x)\,dx$

Published on 26 Mar 2026 - 6:30

score 117 · Answer 11 · 2026-03-25 07:40:19

117

Views

Wald's test. Hypothesis testing. Verification.

Published on 25 Mar 2026 - 7:40

score 55 · Answer 12 · 2026-03-29 16:54:20

55

Views

Isomorphism normal quotient subgroups

Published on 29 Mar 2026 - 16:54

score 67 · Answer 13 · 2018-05-03 14:33:01

67

Views

Prove that if $f,g:\{0,...,n\}\to\mathbb{R}$ are two strictly increasing functions with the same image then it must be the case that $f=g$

Published on 03 May 2018 - 14:33

score 282 · Answer 14 · 2026-03-29 16:47:45

282

Views

Proving an isomorphism using the isomorphism theorems

Published on 29 Mar 2026 - 16:47

score 84 · Answer 15 · 2018-05-03 19:10:57

84

Views

Limit proof using epsilon-delta

Published on 03 May 2018 - 19:10

List Question

Show that if $R$ is an integral domain, then $R[x]$ is an integral domain

Proof verification: There exists a positive real number $x$ such that $x^2=2$

Step by step explaintions needed for integral problems

Assume that the ring $R$ has a commutative multiplication. Prove that the set of nilpotent elements $N$ forms a subring of $R$

Result comparison of a trigonometric equation

Proof verification: Diffeomorphism is an isometry if and only if it preserves the arclength of a parametrised curve.

Necessity of data smoothness for abstract parabolic IVP

How can one prove that $\sqrt{ 2} \cdot \sqrt{ 3} = \sqrt{ 6}$?

Proof check in Linear Algebra with Diagonalizable operator

Fourier transform identity. $\int\limits_{-\infty}^{\infty}\hat f(x)g(x)\,dx=\int\limits_{-\infty}^{\infty} f(x)\hat g(x)\,dx$

Wald's test. Hypothesis testing. Verification.

Isomorphism normal quotient subgroups

Prove that if $f,g:\{0,...,n\}\to\mathbb{R}$ are two strictly increasing functions with the same image then it must be the case that $f=g$

Proving an isomorphism using the isomorphism theorems

Limit proof using epsilon-delta

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