Question

Let $I$ be an ideal of a ring $R$. Then Show that $|(R/I)| = 1 $ if and only if $R = I$.

score 68 · Answer 1 · 2016-02-14 17:50:13

68

Views

Let $I$ be an ideal of a ring $R$. Then Show that $|(R/I)| = 1 $ if and only if $R = I$.

Published on 14 Feb 2016 - 17:50

score 120 · Answer 2 · 2016-02-17 00:03:22

120

Views

More elegant way to make the argument that $\mathbb{Q}[x,y]/\langle x,y \rangle \cong \mathbb{Q}$

Published on 17 Feb 2016 - 0:03

score 136 · Answer 3 · 2016-02-19 18:04:39

136

Views

Proving that there is no ideal $I$ in $\mathbb{Z}[t]$ such that $\mathbb{Z}[t]/I \cong \mathbb{Q}$

Published on 19 Feb 2016 - 18:04

score 106 · Answer 4 · 2026-03-30 05:16:26

106

Views

Covering Projections and Quotients

Published on 30 Mar 2026 - 5:16

score 716 · Answer 5 · 2016-02-20 23:40:10

716

Views

Exercise involving the quotient topology

Published on 20 Feb 2016 - 23:40

score 765 · Answer 6 · 2016-02-22 03:58:50

765

Views

A quotient topology exercise.

Published on 22 Feb 2016 - 3:58

score 115 · Answer 7 · 2016-02-26 00:38:37

115

Views

$V$ is vector space of polynomials $\mathbb R[X]_{<4}$. Let $U = \{P \in V : P(3) = 0\}$. Find a basis of $V/U$.

Published on 26 Feb 2016 - 0:38

score 194 · Answer 8 · 2016-02-28 12:56:49

194

Views

Geometrical intuition of quotient spaces

Published on 28 Feb 2016 - 12:56

score 53 · Answer 9 · 2016-02-29 00:13:44

53

Views

Show that $[a][\star][b] :=[a \star b]$ defines an operation on $G/\sim$.

Published on 29 Feb 2016 - 0:13

score 259 · Answer 10 · 2016-03-02 14:03:42

259

Views

Continuous map from topological space $A\rightarrow B$ as composition of quotient map and unique continuous map from quotient space to $B$

Published on 02 Mar 2016 - 14:03

score 498 · Answer 11 · 2026-03-09 09:15:35

498

Views

Quotient map for space of leaves of a foliation

Published on 09 Mar 2026 - 9:15

score 176 · Answer 12 · 2016-03-08 11:40:08

176

Views

Trying to understand the proof for complements of subspaces of finite codimension

Published on 08 Mar 2016 - 11:40

score 70 · Answer 13 · 2016-03-09 13:05:14

70

Views

The quotient group (space) of $\Bbb Z/H$

Published on 09 Mar 2016 - 13:05

score 138 · Answer 14 · 2026-03-27 05:34:44

138

Views

Proving that a specific map exists

Published on 27 Mar 2026 - 5:34

score 331 · Answer 15 · 2016-03-10 01:10:54

331

Views

The function that identifies the closed unit ball in $R^2$ to $S^2$

Published on 10 Mar 2016 - 1:10

List Question

Let $I$ be an ideal of a ring $R$. Then Show that $|(R/I)| = 1 $ if and only if $R = I$.

More elegant way to make the argument that $\mathbb{Q}[x,y]/\langle x,y \rangle \cong \mathbb{Q}$

Proving that there is no ideal $I$ in $\mathbb{Z}[t]$ such that $\mathbb{Z}[t]/I \cong \mathbb{Q}$

Covering Projections and Quotients

Exercise involving the quotient topology

A quotient topology exercise.

$V$ is vector space of polynomials $\mathbb R[X]_{<4}$. Let $U = \{P \in V : P(3) = 0\}$. Find a basis of $V/U$.

Geometrical intuition of quotient spaces

Show that $[a][\star][b] :=[a \star b]$ defines an operation on $G/\sim$.

Continuous map from topological space $A\rightarrow B$ as composition of quotient map and unique continuous map from quotient space to $B$

Quotient map for space of leaves of a foliation

Trying to understand the proof for complements of subspaces of finite codimension

The quotient group (space) of $\Bbb Z/H$

Proving that a specific map exists

The function that identifies the closed unit ball in $R^2$ to $S^2$

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