Question

Can an integral domain have an element that has no square root but has a square root in the field of fractions?

score 482 · Answer 1 · 2026-03-28 15:21:27

482

Views

Can an integral domain have an element that has no square root but has a square root in the field of fractions?

Published on 28 Mar 2026 - 15:21

score 176 · Answer 2 · 2026-03-29 22:31:39

176

Views

A sequence $\{a_n\}$ that diverges but $\displaystyle\lim_{n\to 0} |a_n-a_{n+1}| =0$

Published on 29 Mar 2026 - 22:31

score 3.4k · Answer 3 · 2016-12-13 21:53:43

3.4k

Views

Isomorphic groups but not isomorphic rings

Published on 13 Dec 2016 - 21:53

score 59 · Answer 4 · 2026-03-31 06:53:19

59

Views

Is $\prod_{i=1}^{n}x_{i} > \prod_{i=1}^{n}y_{i} \implies \prod_{i=1}^{n}(x_{i}+k) > \prod_{i=1}^{n}(y_{i}+k)$ true?

Published on 31 Mar 2026 - 6:53

score 10.6k · Answer 5 · 2026-03-26 08:04:20

10.6k

Views

What are some examples of infinite nonabelian groups?

Published on 26 Mar 2026 - 8:04

score 102 · Answer 6 · 2016-12-16 12:28:20

102

Views

If $A\oplus B\cong A\oplus C$ and $A$ is simple, does it follow that $B\cong C$

Published on 16 Dec 2016 - 12:28

score 221 · Answer 7 · 2026-03-31 19:13:33

221

Views

Independent with a vector v.s. independent with its components

Published on 31 Mar 2026 - 19:13

score 508 · Answer 8 · 2026-04-02 11:43:04

508

Views

Transitive, Reflexive, Symmetric Relations

Published on 02 Apr 2026 - 11:43

score 1k · Answer 9 · 2016-12-17 22:26:34

1k

Views

Examples for $f(\bar A)\subsetneq\overline{f(A)}$ with $f$ being continuous

Published on 17 Dec 2016 - 22:26

score 60 · Answer 10 · 2016-12-19 04:54:32

60

Views

Topological space $X$ which every non-constant real-valued continuous function on $X$ is unbounded.

Published on 19 Dec 2016 - 4:54

score 238 · Answer 11 · 2026-02-23 13:31:48

238

Views

Pullback lemma counterexample

Published on 23 Feb 2026 - 13:31

score 655 · Answer 12 · 2026-03-31 21:07:11

655

Views

Exhibit a non-principal ideal

Published on 31 Mar 2026 - 21:07

score 133 · Answer 13 · 2026-04-02 22:10:00

133

Views

Example of function in $L^1(S^1,\mathbb{R})$ but not in $\operatorname{BMO}(S^1,\mathbb{R})$

Published on 02 Apr 2026 - 22:10

score 6.7k · Answer 14 · 2016-12-21 03:02:55

6.7k

Views

Subspaces of $\ell^{2}$ and $\ell^{\infty}$ which are not closed?

Published on 21 Dec 2016 - 3:02

score 947 · Answer 15 · 2026-04-02 14:42:29

947

Views

Connected topological space such that the removal of any of its points disconnects it into exactly $3$ connected components?

Published on 02 Apr 2026 - 14:42

List Question

Can an integral domain have an element that has no square root but has a square root in the field of fractions?

A sequence $\{a_n\}$ that diverges but $\displaystyle\lim_{n\to 0} |a_n-a_{n+1}| =0$

Isomorphic groups but not isomorphic rings

Is $\prod_{i=1}^{n}x_{i} > \prod_{i=1}^{n}y_{i} \implies \prod_{i=1}^{n}(x_{i}+k) > \prod_{i=1}^{n}(y_{i}+k)$ true?

What are some examples of infinite nonabelian groups?

If $A\oplus B\cong A\oplus C$ and $A$ is simple, does it follow that $B\cong C$

Independent with a vector v.s. independent with its components

Transitive, Reflexive, Symmetric Relations

Examples for $f(\bar A)\subsetneq\overline{f(A)}$ with $f$ being continuous

Topological space $X$ which every non-constant real-valued continuous function on $X$ is unbounded.

Pullback lemma counterexample

Exhibit a non-principal ideal

Example of function in $L^1(S^1,\mathbb{R})$ but not in $\operatorname{BMO}(S^1,\mathbb{R})$

Subspaces of $\ell^{2}$ and $\ell^{\infty}$ which are not closed?

Connected topological space such that the removal of any of its points disconnects it into exactly $3$ connected components?

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