Question

Given ideal $I \subset$ $ \mathbb{R}[X]$ contains the polynomials $X^2 + 1$ and $X^5+X+1$ show that $I =\mathbb R[X]$

score 70 · Answer 1 · 2016-11-14 22:44:22

70

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Given ideal $I \subset$ $ \mathbb{R}[X]$ contains the polynomials $X^2 + 1$ and $X^5+X+1$ show that $I =\mathbb R[X]$

Published on 14 Nov 2016 - 22:44

score 80 · Answer 2 · 2016-11-15 17:48:52

80

Views

Set of Polynomials in Q[x] vanish on {1,2,3} is an ideal in Q[x]

Published on 15 Nov 2016 - 17:48

score 2k · Answer 3 · 2026-03-31 17:47:54

2k

Views

Prime ideals of the matrix ring

Published on 31 Mar 2026 - 17:47

score 700 · Answer 4 · 2026-02-24 15:36:37

700

Views

$n$ by $n$ matrices such that $Ax=0$ implies $Bx=0$, then what can we say about $A$ and $B$?

Published on 24 Feb 2026 - 15:36

score 1.6k · Answer 5 · 2026-03-30 12:40:12

1.6k

Views

Can you define a greatest common divisor in a commutative ring that is not a domain?

Published on 30 Mar 2026 - 12:40

score 364 · Answer 6 · 2026-03-31 17:43:55

364

Views

Prime matrix rings

Published on 31 Mar 2026 - 17:43

score 528 · Answer 7 · 2016-11-17 16:18:28

528

Views

Ideals and Filters are closed under Arbitrary intersection and Arbitrary union respectively

Published on 17 Nov 2016 - 16:18

score 46 · Answer 8 · 2016-11-17 22:57:25

46

Views

Is it still a ramified ideal when the generating prime number seems to split?

Published on 17 Nov 2016 - 22:57

score 1.3k · Answer 9 · 2026-03-31 17:49:02

1.3k

Views

Intersection of Maximal Ideals of a Ring

Published on 31 Mar 2026 - 17:49

score 72 · Answer 10 · 2016-11-18 16:42:55

72

Views

Ideals in projective space

Published on 18 Nov 2016 - 16:42

score 103 · Answer 11 · 2026-03-31 17:45:12

103

Views

prime ideal behaves like a submodule?

Published on 31 Mar 2026 - 17:45

score 52 · Answer 12 · 2016-11-18 21:15:24

52

Views

Explicitation of an isomorphism between two rings

Published on 18 Nov 2016 - 21:15

score 64 · Answer 13 · 2026-03-31 17:50:42

64

Views

Showing √I is a Subgroup of Prime Ideal in R

Published on 31 Mar 2026 - 17:50

score 1.7k · Answer 14 · 2026-03-31 19:14:55

1.7k

Views

Prime and Maximal Ideals of $\mathbb{Z}_2 \times \mathbb{Z}_4$

Published on 31 Mar 2026 - 19:14

score 91 · Answer 15 · 2016-11-21 22:22:20

91

Views

Submodules of $\mathbb{Q}\oplus \mathbb{Q}$

Published on 21 Nov 2016 - 22:22

List Question

Given ideal $I \subset$ $ \mathbb{R}[X]$ contains the polynomials $X^2 + 1$ and $X^5+X+1$ show that $I =\mathbb R[X]$

Set of Polynomials in Q[x] vanish on {1,2,3} is an ideal in Q[x]

Prime ideals of the matrix ring

$n$ by $n$ matrices such that $Ax=0$ implies $Bx=0$, then what can we say about $A$ and $B$?

Can you define a greatest common divisor in a commutative ring that is not a domain?

Prime matrix rings

Ideals and Filters are closed under Arbitrary intersection and Arbitrary union respectively

Is it still a ramified ideal when the generating prime number seems to split?

Intersection of Maximal Ideals of a Ring

Ideals in projective space

prime ideal behaves like a submodule?

Explicitation of an isomorphism between two rings

Showing √I is a Subgroup of Prime Ideal in R

Prime and Maximal Ideals of $\mathbb{Z}_2 \times \mathbb{Z}_4$

Submodules of $\mathbb{Q}\oplus \mathbb{Q}$

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