Question

Prove that every nonzero element of R is either a unit or a zero–divisor.

score 765 · Answer 1 · 2026-03-25 19:58:59

765

Views

Prove that every nonzero element of R is either a unit or a zero–divisor.

Published on 25 Mar 2026 - 19:58

score 658 · Answer 2 · 2026-03-25 11:06:18

658

Views

$\forall n \in \mathbb{N}, n$ is even $\Leftrightarrow n+1$ is odd

Published on 25 Mar 2026 - 11:06

score 130 · Answer 3 · 2018-03-27 15:08:46

130

Views

Is there a proof by "reverse construction"?

Published on 27 Mar 2018 - 15:08

score 51 · Answer 4 · 2018-03-27 15:41:08

51

Views

Relationship between a compact set $C$ as a subset of an open set $A$. ($C \subset A$)

Published on 27 Mar 2018 - 15:41

score 1.9k · Answer 5 · 2026-03-25 01:18:25

1.9k

Views

For ring homomorphism $\phi:R\to S$, prove that $\phi(R)$ is a subring of $S$.

Published on 25 Mar 2026 - 1:18

score 52 · Answer 6 · 2018-03-27 23:24:30

52

Views

Help with derivative on $\mathbb{R}^{n}$

Published on 27 Mar 2018 - 23:24

score 405 · Answer 7 · 2026-03-25 05:01:13

405

Views

Showing that the projection map $\mathbb{R^2}\to\mathbb{R}, (x,y)\mapsto x$ is continuous

Published on 25 Mar 2026 - 5:01

score 24 · Answer 8 · 2026-03-25 03:00:56

24

Views

On proving that $[0,\alpha)$ is $T_4$, for $\alpha$ ordinal

Published on 25 Mar 2026 - 3:00

score 320 · Answer 9 · 2026-03-19 18:29:00

320

Views

Showing $(3 + \sqrt{3})$ is not a prime ideal in $\mathbb{Z}[\sqrt{3}]$

Published on 19 Mar 2026 - 18:29

score 334 · Answer 10 · 2018-03-28 07:59:45

334

Views

Moore plane / Niemytzki plane and the closed $G_\delta$ subspaces.

Published on 28 Mar 2018 - 7:59

score 152 · Answer 11 · 2018-03-28 10:00:27

152

Views

Is my proof that $f[f^{-1}[B]] = B$ iff $B \subseteq \operatorname{Rng}(f)$ correct?

Published on 28 Mar 2018 - 10:00

score 398 · Answer 12 · 2026-03-25 06:04:10

398

Views

Prove that $(0 ,1)\cap\mathbb{Q}$ is order-isomorphc to $\mathbb{Q}$: is my proof correct?

Published on 25 Mar 2026 - 6:04

score 46 · Answer 13 · 2018-03-28 10:40:20

46

Views

The proof that if $a_{1}>1$ and $a_{n+1}=2-\frac{1}{a_{n}}$ for $n\geq 1$, then $\{a_{n}\}$ is monotone

Published on 28 Mar 2018 - 10:40

score 163 · Answer 14 · 2026-03-27 20:19:45

163

Views

Compactness is preserved by continuous surjections.

Published on 27 Mar 2026 - 20:19

score 26 · Answer 15 · 2018-03-28 13:34:01

26

Views

Derivation of a vector-valued function

Published on 28 Mar 2018 - 13:34

List Question

Prove that every nonzero element of R is either a unit or a zero–divisor.

$\forall n \in \mathbb{N}, n$ is even $\Leftrightarrow n+1$ is odd

Is there a proof by "reverse construction"?

Relationship between a compact set $C$ as a subset of an open set $A$. ($C \subset A$)

For ring homomorphism $\phi:R\to S$, prove that $\phi(R)$ is a subring of $S$.

Help with derivative on $\mathbb{R}^{n}$

Showing that the projection map $\mathbb{R^2}\to\mathbb{R}, (x,y)\mapsto x$ is continuous

On proving that $[0,\alpha)$ is $T_4$, for $\alpha$ ordinal

Showing $(3 + \sqrt{3})$ is not a prime ideal in $\mathbb{Z}[\sqrt{3}]$

Moore plane / Niemytzki plane and the closed $G_\delta$ subspaces.

Is my proof that $f[f^{-1}[B]] = B$ iff $B \subseteq \operatorname{Rng}(f)$ correct?

Prove that $(0 ,1)\cap\mathbb{Q}$ is order-isomorphc to $\mathbb{Q}$: is my proof correct?

The proof that if $a_{1}>1$ and $a_{n+1}=2-\frac{1}{a_{n}}$ for $n\geq 1$, then $\{a_{n}\}$ is monotone

Compactness is preserved by continuous surjections.

Derivation of a vector-valued function

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