Question

Prove that a polynomial ring over R in inﬁnitely many variables is non-Noetherian.

score 506 · Answer 1 · 2026-03-28 08:32:18

506

Views

Prove that a polynomial ring over R in inﬁnitely many variables is non-Noetherian.

Published on 28 Mar 2026 - 8:32

score 98 · Answer 2 · 2018-05-02 15:27:27

98

Views

Finding $(x-1)^{-2}$ in Quotient Ring

Published on 02 May 2018 - 15:27

score 1k · Answer 3 · 2018-05-02 15:55:20

1k

Views

What is the difference between $\Bbb F_4$ and $\Bbb Z/4\Bbb Z$

Published on 02 May 2018 - 15:55

score 708 · Answer 4 · 2018-05-02 19:52:26

708

Views

Can integral domain be trivial? (error in Herstein's Topics in Algebra)

Published on 02 May 2018 - 19:52

score 325 · Answer 5 · 2018-05-02 19:52:31

325

Views

Properties of associates in an integral domain (Ring theory)

Published on 02 May 2018 - 19:52

score 3.5k · Answer 6 · 2018-05-02 20:11:41

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 02 May 2018 - 20:11

score 272 · Answer 7 · 2018-05-02 23:17:59

272

Views

Prime ideals in $\mathbb{C}[f(t),g(t)]$, where $f(t),g(t) \in \mathbb{C}[t]$.

Published on 02 May 2018 - 23:17

score 186 · Answer 8 · 2026-03-28 08:35:39

186

Views

$M_a=\{f\in C[0,1]~:~f(a)=0\}\ne\langle x-a\rangle$

Published on 28 Mar 2026 - 8:35

score 59 · Answer 9 · 2018-05-03 04:25:56

59

Views

Rings in which the "mistake" $(x + y) / d = x / d + y$ is justified

Published on 03 May 2018 - 4:25

score 107 · Answer 10 · 2018-05-03 06:55:37

107

Views

Is it true that in simple rings every regular element is invertible?

Published on 03 May 2018 - 6:55

score 283 · Answer 11 · 2026-03-25 20:10:56

283

Views

Prime Ideal Properly Contained in principal Ideal.

Published on 25 Mar 2026 - 20:10

score 141 · Answer 12 · 2026-03-25 01:15:01

141

Views

Noether normalization: what is a finite map?

Published on 25 Mar 2026 - 1:15

score 56 · Answer 13 · 2026-03-27 06:05:29

56

Views

About free modules

Published on 27 Mar 2026 - 6:05

score 1.9k · Answer 14 · 2026-03-26 12:51:59

1.9k

Views

Show $\mathbb{Q}$ is not a projective $\mathbb{Z}$ module.

Published on 26 Mar 2026 - 12:51

score 522 · Answer 15 · 2026-03-26 07:31:47

522

Views

Why is $0$ a zero divisor?

Published on 26 Mar 2026 - 7:31

List Question

Prove that a polynomial ring over R in inﬁnitely many variables is non-Noetherian.

Finding $(x-1)^{-2}$ in Quotient Ring

What is the difference between $\Bbb F_4$ and $\Bbb Z/4\Bbb Z$

Can integral domain be trivial? (error in Herstein's Topics in Algebra)

Properties of associates in an integral domain (Ring theory)

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

Prime ideals in $\mathbb{C}[f(t),g(t)]$, where $f(t),g(t) \in \mathbb{C}[t]$.

$M_a=\{f\in C[0,1]~:~f(a)=0\}\ne\langle x-a\rangle$

Rings in which the "mistake" $(x + y) / d = x / d + y$ is justified

Is it true that in simple rings every regular element is invertible?

Prime Ideal Properly Contained in principal Ideal.

Noether normalization: what is a finite map?

About free modules

Show $\mathbb{Q}$ is not a projective $\mathbb{Z}$ module.

Why is $0$ a zero divisor?

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