Question

Show $\mathbb Z[x]/(x^2-cx) \ncong \mathbb Z \times \mathbb Z$.

score 1.5k · Answer 1 · 2026-03-25 17:22:54

1.5k

Views

Show $\mathbb Z[x]/(x^2-cx) \ncong \mathbb Z \times \mathbb Z$.

Published on 25 Mar 2026 - 17:22

score 72 · Answer 2 · 2026-04-13 02:35:25

72

Views

Is this statement true?(product and quotient of the groups and rings)

Published on 13 Apr 2026 - 2:35

score 156 · Answer 3 · 2026-04-15 04:21:13

156

Views

Why these are isomorphic each other for given these rings?

Published on 15 Apr 2026 - 4:21

score 83 · Answer 4 · 2026-04-16 02:55:59

83

Views

What is the order of this quotient ring?

Published on 16 Apr 2026 - 2:55

score 499 · Answer 5 · 2026-03-26 03:01:42

499

Views

Does the cancellation property for a group mean something different than the cancellation property for an integral domain?

Published on 26 Mar 2026 - 3:01

score 133 · Answer 6 · 2026-04-14 03:30:16

133

Views

Small's example of left hereditary ring but not right hereditary

Published on 14 Apr 2026 - 3:30

score 131 · Answer 7 · 2026-04-15 17:26:18

131

Views

Question about the necessity of the distributive property axiom used in the definition of a ring

Published on 15 Apr 2026 - 17:26

score 94 · Answer 8 · 2026-03-25 17:41:59

94

Views

Show that there is exactly one ring homomorphism $(\Bbb{Z}/3\Bbb{Z})\times(\Bbb{Z}/4\Bbb{Z})\to\Bbb{Z}/12\Bbb{Z}.$

Published on 25 Mar 2026 - 17:41

score 133 · Answer 9 · 2026-05-11 07:47:27

133

Views

Exploring the isomorphisms of the group algebra $KG$

Published on 11 May 2026 - 7:47

score 74 · Answer 10 · 2026-04-12 00:03:29

74

Views

In every local ring exist nonzero nilpotent ideals?

Published on 12 Apr 2026 - 0:03

score 56 · Answer 11 · 2026-04-12 12:46:28

56

Views

Why is the first Goldie theorem true?

Published on 12 Apr 2026 - 12:46

score 71 · Answer 12 · 2026-04-12 19:18:04

71

Views

Product of the ideal and normal groups(Is this solution right?)

Published on 12 Apr 2026 - 19:18

score 68 · Answer 13 · 2026-04-16 01:21:14

68

Views

Find the isomorphic ring and its order with $\mathbb{Z_{15}}[x] / \langle 3x^2 + 5x \rangle $

Published on 16 Apr 2026 - 1:21

score 54 · Answer 14 · 2026-04-11 04:03:42

54

Views

Is it true for finding the order of $\mathbb{Z}_n[x]/ \langle f(x) \rangle$?

Published on 11 Apr 2026 - 4:03

score 217 · Answer 15 · 2026-05-06 03:11:32

217

Views

Subring of discrete valuation ring is Noetherian?

Published on 06 May 2026 - 3:11

List Question

Show $\mathbb Z[x]/(x^2-cx) \ncong \mathbb Z \times \mathbb Z$.

Is this statement true?(product and quotient of the groups and rings)

Why these are isomorphic each other for given these rings?

What is the order of this quotient ring?

Does the cancellation property for a group mean something different than the cancellation property for an integral domain?

Small's example of left hereditary ring but not right hereditary

Question about the necessity of the distributive property axiom used in the definition of a ring

Show that there is exactly one ring homomorphism $(\Bbb{Z}/3\Bbb{Z})\times(\Bbb{Z}/4\Bbb{Z})\to\Bbb{Z}/12\Bbb{Z}.$

Exploring the isomorphisms of the group algebra $KG$

In every local ring exist nonzero nilpotent ideals?

Why is the first Goldie theorem true?

Product of the ideal and normal groups(Is this solution right?)

Find the isomorphic ring and its order with $\mathbb{Z_{15}}[x] / \langle 3x^2 + 5x \rangle $

Is it true for finding the order of $\mathbb{Z}_n[x]/ \langle f(x) \rangle$?

Subring of discrete valuation ring is Noetherian?

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