Question

Are multilinear polynomial ideals (where $x^2 = x$) necessarily radical?

score 92 · Answer 1 · 2023-10-31 01:27:43

92

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Are multilinear polynomial ideals (where $x^2 = x$) necessarily radical?

Published on 31 Oct 2023 - 1:27

score 24 · Answer 2 · 2026-03-28 10:29:20

24

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Let $I$ be a semiprime ideal of $\mathbf{A}$. Suppose $a\mathbf{A}a \subseteq I$ for some $a$. Show that $a \in I$.

Published on 28 Mar 2026 - 10:29

score 97 · Answer 3 · 2026-04-09 05:10:39

97

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Is $\mathbb Z[x^2]$ an ideal of $\mathbb Z[x]$?

Published on 09 Apr 2026 - 5:10

score 72 · Answer 4 · 2026-04-01 13:31:17

72

Views

Ideals of rings of continuous functions with compact support.

Published on 01 Apr 2026 - 13:31

score 74 · Answer 5 · 2026-03-28 08:35:36

74

Views

The set of all polynomials whose coefficient of $x^2$ is a multiple of 3.

Published on 28 Mar 2026 - 8:35

score 63 · Answer 6 · 2023-11-02 11:50:19

63

Views

Is there a proof for the existence of a complete flag of solvable Lie algebras independet on lie's theorem?

Published on 02 Nov 2023 - 11:50

score 29 · Answer 7 · 2023-11-03 10:15:46

29

Views

Is commutativity of the ring $R$ essential in the above result? Justify.

Published on 03 Nov 2023 - 10:15

score 47 · Answer 8 · 2026-03-26 10:43:29

47

Views

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 26 Mar 2026 - 10:43

score 86 · Answer 9 · 2026-03-29 14:35:30

86

Views

Let $R$ be a factorial ring in which every ideal generated by two elements is a principal ideal. Show that $R$ is a principal ideal ring.

Published on 29 Mar 2026 - 14:35

score 125 · Answer 10 · 2023-11-07 09:49:35

125

Views

Ideal in polynomial rings: When changing the basis, can we bound the degree of coefficients?

Published on 07 Nov 2023 - 9:49

score 97 · Answer 11 · 2026-03-25 04:38:05

97

Views

What information does the numerical norm provide (and why)?

Published on 25 Mar 2026 - 4:38

score 87 · Answer 12 · 2026-04-06 20:54:29

87

Views

Rings where finitely generated ideals are closed under countable intersection

Published on 06 Apr 2026 - 20:54

score 87 · Answer 13 · 2026-03-26 11:47:56

87

Views

Prime avoidance for graded Noetherian ring with infinite residue field.

Published on 26 Mar 2026 - 11:47

score 52 · Answer 14 · 2026-03-27 21:36:30

52

Views

How is quotient of the tensor algebra calculated to form the exterior algebra

Published on 27 Mar 2026 - 21:36

score 167 · Answer 15 · 2023-11-14 03:02:10

167

Views

For ideal $I$, If $rI = I$ what is $r$?

Published on 14 Nov 2023 - 3:02

List Question

Are multilinear polynomial ideals (where $x^2 = x$) necessarily radical?

Let $I$ be a semiprime ideal of $\mathbf{A}$. Suppose $a\mathbf{A}a \subseteq I$ for some $a$. Show that $a \in I$.

Is $\mathbb Z[x^2]$ an ideal of $\mathbb Z[x]$?

Ideals of rings of continuous functions with compact support.

The set of all polynomials whose coefficient of $x^2$ is a multiple of 3.

Is there a proof for the existence of a complete flag of solvable Lie algebras independet on lie's theorem?

Is commutativity of the ring $R$ essential in the above result? Justify.

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.

Let $R$ be a factorial ring in which every ideal generated by two elements is a principal ideal. Show that $R$ is a principal ideal ring.

Ideal in polynomial rings: When changing the basis, can we bound the degree of coefficients?

What information does the numerical norm provide (and why)?

Rings where finitely generated ideals are closed under countable intersection

Prime avoidance for graded Noetherian ring with infinite residue field.

How is quotient of the tensor algebra calculated to form the exterior algebra

For ideal $I$, If $rI = I$ what is $r$?

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