Question

Are the units of a ring $\Bbb {Z}_n, +, •$ also the generators of the cyclic group $\Bbb{Z}_n, + $

score 303 · Answer 1 · 2026-03-28 05:23:14

303

Views

Are the units of a ring $\Bbb {Z}_n, +, •$ also the generators of the cyclic group $\Bbb{Z}_n, + $

Published on 28 Mar 2026 - 5:23

score 178 · Answer 2 · 2026-03-25 14:25:46

178

Views

Is this a correct equivalent formulation of the universal property of the polynomial ring?

Published on 25 Mar 2026 - 14:25

score 96 · Answer 3 · 2026-04-03 13:35:23

96

Views

Proving $\text{Hom}_{R-\text{Mod}}(R^{\oplus A}, R)$ is a product of $A$ copies of $R$

Published on 03 Apr 2026 - 13:35

score 80 · Answer 4 · 2026-03-26 11:17:25

80

Views

Prove Euler totient $\phi(p^k)=p^k(1-\frac{1}{p})$ with group theory?

Published on 26 Mar 2026 - 11:17

score 452 · Answer 5 · 2019-08-16 06:14:24

452

Views

$\operatorname{Spec}k[\epsilon]/(\epsilon^2)$ and $\operatorname{Spec}k[x]_{(x)}$ are both one point

Published on 16 Aug 2019 - 6:14

score 352 · Answer 6 · 2019-08-16 16:00:57

352

Views

Does ring homomorphism from $F_p$ to $\mathbb{Q}$ exist?

Published on 16 Aug 2019 - 16:00

score 196 · Answer 7 · 2026-04-09 23:13:36

196

Views

Explicit description of quotient ring of $\mathbb{Z}[x]$

Published on 09 Apr 2026 - 23:13

score 59 · Answer 8 · 2026-03-25 10:57:10

59

Views

When is $\left\{\begin{pmatrix} x & yb \\ y & x \\ \end{pmatrix} : x,y\in \mathbb{Q}\right\}$ an integral domain?

Published on 25 Mar 2026 - 10:57

score 425 · Answer 9 · 2019-08-17 11:58:15

425

Views

When a maximal ideal is not contained the union of the others

Published on 17 Aug 2019 - 11:58

score 52 · Answer 10 · 2026-03-25 17:20:49

52

Views

localizations of $k[x, y, z]/(x^2 + y^2 + z^2)$

Published on 25 Mar 2026 - 17:20

score 1.5k · Answer 11 · 2019-08-17 13:49:31

1.5k

Views

Yes/ No : The sum of two ideals of a ring R is an ideal of R

Published on 17 Aug 2019 - 13:49

score 50 · Answer 12 · 2019-08-17 16:54:39

50

Views

Prime ideal not containing $r\in R$

Published on 17 Aug 2019 - 16:54

score 67 · Answer 13 · 2019-08-17 17:01:41

67

Views

$k$ is algebraically closed $\Leftrightarrow$ $\forall f \in k[X,Y], V(f)\neq\{(0,0)\}$

Published on 17 Aug 2019 - 17:01

score 209 · Answer 14 · 2026-04-09 02:26:40

209

Views

Elements of $E^{\times},\cdot$ of the quotient ring $E:= \frac{\mathbb{Z}_3[X]}{\langle x^2 + x + 2\rangle}$

Published on 09 Apr 2026 - 2:26

score 19 · Answer 15 · 2019-08-17 20:16:57

19

Views

Prüfer implies that all finitely generated ideals are cancellation ideals

Published on 17 Aug 2019 - 20:16

List Question

Are the units of a ring $\Bbb {Z}_n, +, •$ also the generators of the cyclic group $\Bbb{Z}_n, + $

Is this a correct equivalent formulation of the universal property of the polynomial ring?

Proving $\text{Hom}_{R-\text{Mod}}(R^{\oplus A}, R)$ is a product of $A$ copies of $R$

Prove Euler totient $\phi(p^k)=p^k(1-\frac{1}{p})$ with group theory?

$\operatorname{Spec}k[\epsilon]/(\epsilon^2)$ and $\operatorname{Spec}k[x]_{(x)}$ are both one point

Does ring homomorphism from $F_p$ to $\mathbb{Q}$ exist?

Explicit description of quotient ring of $\mathbb{Z}[x]$

When is $\left\{\begin{pmatrix} x & yb \\ y & x \\ \end{pmatrix} : x,y\in \mathbb{Q}\right\}$ an integral domain?

When a maximal ideal is not contained the union of the others

localizations of $k[x, y, z]/(x^2 + y^2 + z^2)$

Yes/ No : The sum of two ideals of a ring R is an ideal of R

Prime ideal not containing $r\in R$

$k$ is algebraically closed $\Leftrightarrow$ $\forall f \in k[X,Y], V(f)\neq\{(0,0)\}$

Elements of $E^{\times},\cdot$ of the quotient ring $E:= \frac{\mathbb{Z}_3[X]}{\langle x^2 + x + 2\rangle}$

Prüfer implies that all finitely generated ideals are cancellation ideals

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