Question

In the ring $\mathbb{Z}[\sqrt{3}]=\{a+b\sqrt{3}\mid a,b \in \mathbb{Z}\}$, show the following.

score 137 · Answer 1 · 2026-03-25 13:56:52

137

Views

In the ring $\mathbb{Z}[\sqrt{3}]=\{a+b\sqrt{3}\mid a,b \in \mathbb{Z}\}$, show the following.

Published on 25 Mar 2026 - 13:56

score 82 · Answer 2 · 2018-05-15 19:49:17

82

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Specific dimension calculation

Published on 15 May 2018 - 19:49

score 70 · Answer 3 · 2018-05-15 21:01:26

70

Views

Question about a comment on a different question. A rational root of a monic polynomial over $\Bbb Z[x]$ is an integer

Published on 15 May 2018 - 21:01

score 92 · Answer 4 · 2026-03-25 06:23:01

92

Views

Does isomorphism of analytic algebras determine their analytic tensor product (modulo isomorphism)?

Published on 25 Mar 2026 - 6:23

score 30 · Answer 5 · 2026-03-27 10:45:46

30

Views

Does the cyclic algebra construction preserve surjective maps and direct products?

Published on 27 Mar 2026 - 10:45

score 61 · Answer 6 · 2026-03-28 11:53:38

61

Views

Ideal of a ring polynomial?

Published on 28 Mar 2026 - 11:53

score 386 · Answer 7 · 2018-05-17 15:41:42

386

Views

the left inverse and right inverse in a ring

Published on 17 May 2018 - 15:41

score 205 · Answer 8 · 2026-03-27 10:44:17

205

Views

Regular ideals are invertible

Published on 27 Mar 2026 - 10:44

score 811 · Answer 9 · 2026-03-25 04:41:02

811

Views

Proving that $\mathbb{Z}[x]/(x^3-2x+1)$ is not an integral domain and that x is a unit

Published on 25 Mar 2026 - 4:41

score 42 · Answer 10 · 2026-03-28 13:42:09

42

Views

Elements $f \in \mathbb{Z}[X]/I$ which satisfy $f^{18}=1$

Published on 28 Mar 2026 - 13:42

score 533 · Answer 11 · 2026-03-28 04:16:59

533

Views

Epimorphism, in the category of commutative rings with unity , with domain a field is an isomorphism?

Published on 28 Mar 2026 - 4:16

score 620 · Answer 12 · 2018-05-19 22:46:11

620

Views

Is there a non-unital ring such that one of its quotient ring is unital?

Published on 19 May 2018 - 22:46

score 321 · Answer 13 · 2018-05-20 00:31:17

321

Views

Is there a maximal but not ideally prime ideal?

Published on 20 May 2018 - 0:31

score 276 · Answer 14 · 2026-03-28 12:02:38

276

Views

Four part question on two ideals of a ring $R$

Published on 28 Mar 2026 - 12:02

score 79 · Answer 15 · 2026-03-27 12:03:12

79

Views

$R$ a commutative ring of characteristic $n>0$. If there is a monic polynomial in $(\mathbb Z/n)[X]$ vanishing identically on $R$, then $\dim R=0$

Published on 27 Mar 2026 - 12:03

List Question

In the ring $\mathbb{Z}[\sqrt{3}]=\{a+b\sqrt{3}\mid a,b \in \mathbb{Z}\}$, show the following.

Specific dimension calculation

Question about a comment on a different question. A rational root of a monic polynomial over $\Bbb Z[x]$ is an integer

Does isomorphism of analytic algebras determine their analytic tensor product (modulo isomorphism)?

Does the cyclic algebra construction preserve surjective maps and direct products?

Ideal of a ring polynomial?

the left inverse and right inverse in a ring

Regular ideals are invertible

Proving that $\mathbb{Z}[x]/(x^3-2x+1)$ is not an integral domain and that x is a unit

Elements $f \in \mathbb{Z}[X]/I$ which satisfy $f^{18}=1$

Epimorphism, in the category of commutative rings with unity , with domain a field is an isomorphism?

Is there a non-unital ring such that one of its quotient ring is unital?

Is there a maximal but not ideally prime ideal?

Four part question on two ideals of a ring $R$

$R$ a commutative ring of characteristic $n>0$. If there is a monic polynomial in $(\mathbb Z/n)[X]$ vanishing identically on $R$, then $\dim R=0$

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