Question

Characterization of trivial localization of module?

score 111 · Answer 1 · 2026-03-25 14:12:41

111

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Characterization of trivial localization of module?

Published on 25 Mar 2026 - 14:12

score 528 · Answer 2 · 2026-03-23 07:01:31

528

Views

Prove that $\mathbb{Z}_{5}[x]/(x^2+1)$ is isomorphic to $\mathbb{Z}_{5} \times \mathbb{Z}_{5}$.

Published on 23 Mar 2026 - 7:01

score 128 · Answer 3 · 2018-02-13 04:08:54

128

Views

Identify $\mathbb{Z}[x]/(2x^2+1,2x-3)$.

Published on 13 Feb 2018 - 4:08

score 537 · Answer 4 · 2026-03-20 06:43:53

537

Views

Every homomorphism $\varphi : F \to R$ from a field $F$ to a nonzero ring $R$ is injective: proof details in Artin

Published on 20 Mar 2026 - 6:43

score 37 · Answer 5 · 2018-02-13 11:13:00

37

Views

K-Algebras in which every subalgebra generated by single element is one-dimensional

Published on 13 Feb 2018 - 11:13

score 150 · Answer 6 · 2026-03-19 23:26:42

150

Views

On the definition of free algebra and localization of a non-commutative ring

Published on 19 Mar 2026 - 23:26

score 47 · Answer 7 · 2018-02-13 21:36:56

47

Views

Why do we need to require that $0$ is in an ideal?

Published on 13 Feb 2018 - 21:36

score 465 · Answer 8 · 2026-03-22 18:49:33

465

Views

A question about unique factorization domain

Published on 22 Mar 2026 - 18:49

score 64 · Answer 9 · 2026-03-22 05:41:19

64

Views

If the norm of $\alpha \in \mathbb{Z}[i]$ is a square, show that $\alpha$ is a square in $\mathbb{Z}[i]$

Published on 22 Mar 2026 - 5:41

score 793 · Answer 10 · 2026-03-22 17:31:00

793

Views

Commutative Noetherian, local, reduced ring has only one minimal prime ideal?

Published on 22 Mar 2026 - 17:31

score 33 · Answer 11 · 2018-02-15 06:49:49

33

Views

Is this computation correct (dimension of rings, transcendence degree)

Published on 15 Feb 2018 - 6:49

score 59 · Answer 12 · 2026-03-25 03:00:37

59

Views

extension field of $\mathbb{Q}$

Published on 25 Mar 2026 - 3:00

score 61 · Answer 13 · 2026-03-25 15:44:07

61

Views

Show that cardinality of $\mathbb{Z}^n/T(\mathbb{Z}^n)$ equals the absolute value of the determinant of the matrix representing the homomorphism T

Published on 25 Mar 2026 - 15:44

score 271 · Answer 14 · 2018-02-15 11:39:55

271

Views

Proof Verification of Multiplicative Group of $(Z_n,+,\times)$

Published on 15 Feb 2018 - 11:39

score 54 · Answer 15 · 2018-02-15 14:59:49

54

Views

Show $S[[x]]\rightarrow K^{(x)}$ is surjective

Published on 15 Feb 2018 - 14:59

List Question

Characterization of trivial localization of module?

Prove that $\mathbb{Z}_{5}[x]/(x^2+1)$ is isomorphic to $\mathbb{Z}_{5} \times \mathbb{Z}_{5}$.

Identify $\mathbb{Z}[x]/(2x^2+1,2x-3)$.

Every homomorphism $\varphi : F \to R$ from a field $F$ to a nonzero ring $R$ is injective: proof details in Artin

K-Algebras in which every subalgebra generated by single element is one-dimensional

On the definition of free algebra and localization of a non-commutative ring

Why do we need to require that $0$ is in an ideal?

A question about unique factorization domain

If the norm of $\alpha \in \mathbb{Z}[i]$ is a square, show that $\alpha$ is a square in $\mathbb{Z}[i]$

Commutative Noetherian, local, reduced ring has only one minimal prime ideal?

Is this computation correct (dimension of rings, transcendence degree)

extension field of $\mathbb{Q}$

Show that cardinality of $\mathbb{Z}^n/T(\mathbb{Z}^n)$ equals the absolute value of the determinant of the matrix representing the homomorphism T

Proof Verification of Multiplicative Group of $(Z_n,+,\times)$

Show $S[[x]]\rightarrow K^{(x)}$ is surjective

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