Question

Small question about contravariant functors

score 59 · Answer 1 · 2023-09-17 10:24:19

59

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Small question about contravariant functors

Published on 17 Sep 2023 - 10:24

score 52 · Answer 2 · 2023-09-23 02:10:46

52

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$ \left\lfloor\frac{x - \pi(z)^}{n} \right\rfloor\geq\left\lfloor\frac{x-z^}{m}\right\rfloor $ whenever $n\mid m$ and $\pi:\Bbb{Z}/m\to\Bbb{Z}/n$✨

Published on 23 Sep 2023 - 2:10

score 90 · Answer 3 · 2023-09-24 11:57:31

90

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What $\mathbb Z/\ker f$ mean if $f$ is injective?

Published on 24 Sep 2023 - 11:57

score 57 · Answer 4 · 2023-09-26 12:23:33

57

Views

Surjective ring homomorphism from $\mathbb{Z}[\sqrt{-5}]$ to $\mathbb Z/3\mathbb Z$.

Published on 26 Sep 2023 - 12:23

score 65 · Answer 5 · 2023-09-28 18:29:17

65

Views

Commutativity of a ring with a ring homomorphism to itself $f(x) = x^2$

Published on 28 Sep 2023 - 18:29

score 26 · Answer 6 · 2023-10-18 11:38:55

26

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Equivalent statement about the characteristic of a ring

Published on 18 Oct 2023 - 11:38

score 61 · Answer 7 · 2023-10-20 07:06:29

61

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Let $K_1, K_2$ be fields and $f: K_1 \to K_2$ Ring Homomorphism. Prove $f$ is injective or Zero Homomorphism ($f(a) = 0_{K_2}$ for all $a \in K_1$)

Published on 20 Oct 2023 - 7:06

score 29 · Answer 8 · 2023-11-02 02:53:32

29

Views

Relation of ring homomorphism pre-images

Published on 02 Nov 2023 - 2:53

score 46 · Answer 9 · 2023-11-03 10:42:47

46

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Let $R$ and $R'$ be two rings and $f:R\to R'$ be a ring homomorphism. Let $I$ be an ideal of $R.$ Is $f(I)$ an ideal of $R'?$ Justify.

Published on 03 Nov 2023 - 10:42

score 148 · Answer 10 · 2026-03-25 23:39:35

148

Views

Show that: exists unique ring homomorphism $\varphi : \mathbb{Z} [ i ] \longrightarrow R$ with $\varphi ( i ) = a$, where $a^{2} =-1_{R}$

Published on 25 Mar 2026 - 23:39

score 61 · Answer 11 · 2026-03-25 17:37:15

61

Views

On the homomorphism as $M_n(A)$-modules.

Published on 25 Mar 2026 - 17:37

score 56 · Answer 12 · 2024-01-04 20:32:04

56

Views

Is the following transformation h from R to S a ring homomorphism?

Published on 04 Jan 2024 - 20:32

score 107 · Answer 13 · 2024-01-11 10:19:40

107

Views

homomorphism from a (semi)local ring to $\mathbb Z$

Published on 11 Jan 2024 - 10:19

score 59 · Answer 14 · 2024-01-12 15:30:14

59

Views

Check finiteness of ring map with SAGE

Published on 12 Jan 2024 - 15:30

score 113 · Answer 15 · 2024-01-14 10:11:40

113

Views

homomorphisms from a (semi)local ring to a ring with infinitely many maximal ideals

Published on 14 Jan 2024 - 10:11

List Question

Small question about contravariant functors

$ \left\lfloor\frac{x - \pi(z)^}{n} \right\rfloor\geq\left\lfloor\frac{x-z^}{m}\right\rfloor $ whenever $n\mid m$ and $\pi:\Bbb{Z}/m\to\Bbb{Z}/n$✨

What $\mathbb Z/\ker f$ mean if $f$ is injective?

Surjective ring homomorphism from $\mathbb{Z}[\sqrt{-5}]$ to $\mathbb Z/3\mathbb Z$.

Commutativity of a ring with a ring homomorphism to itself $f(x) = x^2$

Equivalent statement about the characteristic of a ring

Let $K_1, K_2$ be fields and $f: K_1 \to K_2$ Ring Homomorphism. Prove $f$ is injective or Zero Homomorphism ($f(a) = 0_{K_2}$ for all $a \in K_1$)

Relation of ring homomorphism pre-images

Let $R$ and $R'$ be two rings and $f:R\to R'$ be a ring homomorphism. Let $I$ be an ideal of $R.$ Is $f(I)$ an ideal of $R'?$ Justify.

Show that: exists unique ring homomorphism $\varphi : \mathbb{Z} [ i ] \longrightarrow R$ with $\varphi ( i ) = a$, where $a^{2} =-1_{R}$

On the homomorphism as $M_n(A)$-modules.

Is the following transformation h from R to S a ring homomorphism?

homomorphism from a (semi)local ring to $\mathbb Z$

Check finiteness of ring map with SAGE

homomorphisms from a (semi)local ring to a ring with infinitely many maximal ideals

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