Question

Understanding the structure of $\mathbb{Z}[[x]]/(x-x^2)$

score 56 · Answer 1 · 2026-03-28 03:26:25

56

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Understanding the structure of $\mathbb{Z}[[x]]/(x-x^2)$

Published on 28 Mar 2026 - 3:26

score 76 · Answer 2 · 2021-10-14 14:44:47

76

Views

A not constant unit in the ring $\mathbb{Z}/27\mathbb{Z}[X]$ and another one in $\mathbb{Z}/96\mathbb{Z}[X]$.

Published on 14 Oct 2021 - 14:44

score 61 · Answer 3 · 2021-10-16 18:51:17

61

Views

Isomorphism from a non trivial ring onto the polynomial ring over itself

Published on 16 Oct 2021 - 18:51

score 56 · Answer 4 · 2021-10-25 06:43:37

56

Views

Faulty proof in the claim "If a polynomial is irreducible in $Z_p [x]$ then it is irreducible in $Z_{p^k} [x]$?

Published on 25 Oct 2021 - 6:43

score 34 · Answer 5 · 2021-11-13 08:58:25

34

Views

Let $J \subset k[x_1,\dots,x_n], V(J) = Z \in \mathbb{A}_k^n$, and $A(Z) := k[x_1,\dots,x_n] /J$. Then $f \in A(Z)$ becomes a function $f: Z \to k^1$.

Published on 13 Nov 2021 - 8:58

score 101 · Answer 6 · 2021-11-16 20:15:08

101

Views

Mapping from $F$ to $E$ where $F$ is a field and $E=F[x]/\langle p(x)\rangle$

Published on 16 Nov 2021 - 20:15

score 37 · Answer 7 · 2021-11-23 11:27:12

37

Views

How to understand $I(\emptyset) = k[x_1,\dots,x_n]$?

Published on 23 Nov 2021 - 11:27

score 99 · Answer 8 · 2021-11-27 20:43:11

99

Views

If a $k$-algebra $R$ is isomorphic to $k[x_1,\dots,x_n]/J$ (where $J$ is an ideal), then $R$ is finitely generated.

Published on 27 Nov 2021 - 20:43

score 51 · Answer 9 · 2026-03-27 07:35:38

51

Views

T[x] Euclidean if and only if T is a field.

Published on 27 Mar 2026 - 7:35

score 147 · Answer 10 · 2021-12-10 14:38:18

147

Views

Domain containing polynomial ring over field, if finitely generated generated as module over it, is free as module over it

Published on 10 Dec 2021 - 14:38

score 59 · Answer 11 · 2021-12-11 17:59:37

59

Views

Issues with ideals

Published on 11 Dec 2021 - 17:59

score 544 · Answer 12 · 2021-12-13 20:31:49

544

Views

Is $\Bbb Z_4 [X]$ an integral domain?

Published on 13 Dec 2021 - 20:31

score 249 · Answer 13 · 2021-12-25 18:23:01

249

Views

if every finitely generated $R$-module has Finite Free Resolution, then every finitely generated $R[x]$-module also has it

Published on 25 Dec 2021 - 18:23

score 99 · Answer 14 · 2021-12-27 16:03:47

99

Views

Rational functions: unique representation as a polynomial fraction?

Published on 27 Dec 2021 - 16:03

score 42 · Answer 15 · 2021-12-30 20:44:24

42

Views

Let $D$ be an integral domain and let $c\in D$ be irreducible in $D$. Show the ideal $(x,c)$ in $D[x]$ is not principal.

Published on 30 Dec 2021 - 20:44

List Question

Understanding the structure of $\mathbb{Z}[[x]]/(x-x^2)$

A not constant unit in the ring $\mathbb{Z}/27\mathbb{Z}[X]$ and another one in $\mathbb{Z}/96\mathbb{Z}[X]$.

Isomorphism from a non trivial ring onto the polynomial ring over itself

Faulty proof in the claim "If a polynomial is irreducible in $Z_p [x]$ then it is irreducible in $Z_{p^k} [x]$?

Let $J \subset k[x_1,\dots,x_n], V(J) = Z \in \mathbb{A}_k^n$, and $A(Z) := k[x_1,\dots,x_n] /J$. Then $f \in A(Z)$ becomes a function $f: Z \to k^1$.

Mapping from $F$ to $E$ where $F$ is a field and $E=F[x]/\langle p(x)\rangle$

How to understand $I(\emptyset) = k[x_1,\dots,x_n]$?

If a $k$-algebra $R$ is isomorphic to $k[x_1,\dots,x_n]/J$ (where $J$ is an ideal), then $R$ is finitely generated.

T[x] Euclidean if and only if T is a field.

Domain containing polynomial ring over field, if finitely generated generated as module over it, is free as module over it

Issues with ideals

Is $\Bbb Z_4 [X]$ an integral domain?

if every finitely generated $R$-module has Finite Free Resolution, then every finitely generated $R[x]$-module also has it

Rational functions: unique representation as a polynomial fraction?

Let $D$ be an integral domain and let $c\in D$ be irreducible in $D$. Show the ideal $(x,c)$ in $D[x]$ is not principal.

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