Question

ideal I=(x^3,x^5) of the polynomial ring Q[x]

score 53 · Answer 1 · 2019-08-15 14:47:52

53

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ideal I=(x^3,x^5) of the polynomial ring Q[x]

Published on 15 Aug 2019 - 14:47

score 41 · Answer 2 · 2019-08-19 01:46:16

41

Views

Is it possible that an ideal generated by $S$ does not contain $S$?

Published on 19 Aug 2019 - 1:46

score 148 · Answer 3 · 2019-08-20 13:39:33

148

Views

Modular law for ideals in a commutative ring with 1

Published on 20 Aug 2019 - 13:39

score 67 · Answer 4 · 2026-03-25 20:11:12

67

Views

If $e_1,\dots,e_n\in R$ are idempotent then $\langle e_1,\dots,e_n\rangle=\langle d\rangle$ for some idempotent $d\in R$

Published on 25 Mar 2026 - 20:11

score 172 · Answer 5 · 2019-08-20 23:40:52

172

Views

The field of fractions of $\mathbb{R}[x,y]/(x^2+y^2-1)$ is $\mathbb{R}(x)[y]/(x^2+y^2-1)$

Published on 20 Aug 2019 - 23:40

score 81 · Answer 6 · 2026-03-25 17:52:51

81

Views

Elements squaring to zero form an ideal in $\mathbf{Z}/n\mathbf{Z}$

Published on 25 Mar 2026 - 17:52

score 191 · Answer 7 · 2019-08-21 14:45:56

191

Views

Characterization of the integral closure of an ideal in a domain (Exercise 4.14 in Eisenbud)

Published on 21 Aug 2019 - 14:45

score 218 · Answer 8 · 2019-08-21 21:41:58

218

Views

If $R$ is a ring, $K$ a field (and subring of $R$), and $I$ a proper ideal of $R$, $R/I$ contains a field isomorphic to $K$

Published on 21 Aug 2019 - 21:41

score 321 · Answer 9 · 2026-03-27 01:29:51

321

Views

Computing ideal of initial forms

Published on 27 Mar 2026 - 1:29

score 393 · Answer 10 · 2019-08-22 22:49:16

393

Views

The kernel of $\mathbb{Q}[x,y]\rightarrow \mathbb{Q}(t)$ is $(x^2+y^2-1)$.

Published on 22 Aug 2019 - 22:49

score 213 · Answer 11 · 2019-08-23 04:50:50

213

Views

$\mathbb{Q}[x,y]/(x^2+y^2)\cong \mathbb{Q}[y,yi]$?

Published on 23 Aug 2019 - 4:50

score 66 · Answer 12 · 2019-08-25 04:06:11

66

Views

Radical ideals and vector-space dimension of quotient rings

Published on 25 Aug 2019 - 4:06

score 52 · Answer 13 · 2026-03-27 09:48:34

52

Views

class group calculation for $\Bbb Q(i)$

Published on 27 Mar 2026 - 9:48

score 265 · Answer 14 · 2026-03-25 12:50:59

265

Views

$R$ is an algebra over an infinite field. If $\exists$ ideals s.t. $J\subseteq \bigcup_{k=1}^nI_k$ then $J\subseteq I_k$ for some $k$

Published on 25 Mar 2026 - 12:50

score 55 · Answer 15 · 2019-08-27 21:29:17

55

Views

homomorphism from decomposition group to Galois group

Published on 27 Aug 2019 - 21:29

List Question

ideal I=(x^3,x^5) of the polynomial ring Q[x]

Is it possible that an ideal generated by $S$ does not contain $S$?

Modular law for ideals in a commutative ring with 1

If $e_1,\dots,e_n\in R$ are idempotent then $\langle e_1,\dots,e_n\rangle=\langle d\rangle$ for some idempotent $d\in R$

The field of fractions of $\mathbb{R}[x,y]/(x^2+y^2-1)$ is $\mathbb{R}(x)[y]/(x^2+y^2-1)$

Elements squaring to zero form an ideal in $\mathbf{Z}/n\mathbf{Z}$

Characterization of the integral closure of an ideal in a domain (Exercise 4.14 in Eisenbud)

If $R$ is a ring, $K$ a field (and subring of $R$), and $I$ a proper ideal of $R$, $R/I$ contains a field isomorphic to $K$

Computing ideal of initial forms

The kernel of $\mathbb{Q}[x,y]\rightarrow \mathbb{Q}(t)$ is $(x^2+y^2-1)$.

$\mathbb{Q}[x,y]/(x^2+y^2)\cong \mathbb{Q}[y,yi]$?

Radical ideals and vector-space dimension of quotient rings

class group calculation for $\Bbb Q(i)$

$R$ is an algebra over an infinite field. If $\exists$ ideals s.t. $J\subseteq \bigcup_{k=1}^nI_k$ then $J\subseteq I_k$ for some $k$

homomorphism from decomposition group to Galois group

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