Question

Is $\mathbb{Z}[x]\over \langle x+3\rangle$ field?

score 280 · Answer 1 · 2026-04-11 10:49:59

280

Views

Is $\mathbb{Z}[x]\over \langle x+3\rangle$ field?

Published on 11 Apr 2026 - 10:49

score 254 · Answer 2 · 2026-04-13 19:04:15

254

Views

If $JA_{P}\subset IA_{ P}$ for every associated prime, then $J\subset I$

Published on 13 Apr 2026 - 19:04

score 1.4k · Answer 3 · 2026-04-16 07:02:20

1.4k

Views

Any left ideal of $M_n(\mathbb{F})$ is principal

Published on 16 Apr 2026 - 7:02

score 3.2k · Answer 4 · 2026-04-13 04:44:31

3.2k

Views

Determining the structure of the quotient ring $\mathbb{Z}[x]/(x^2+3,p)$

Published on 13 Apr 2026 - 4:44

score 67 · Answer 5 · 2026-04-16 07:34:40

67

Views

Prove that $f:I\oplus J\to R\oplus IJ: (i,j)\mapsto (i+j,ij_0-i_0j)$ is surjective for coprime $I,J$

Published on 16 Apr 2026 - 7:34

score 240 · Answer 6 · 2026-04-15 19:07:21

240

Views

For $\mathfrak{m}$ maximal and principal, there's no ideal between $\mathfrak{m}^2$ and $\mathfrak{m}$

Published on 15 Apr 2026 - 19:07

score 88 · Answer 7 · 2026-04-11 19:16:33

88

Views

an example of a non convex ideal

Published on 11 Apr 2026 - 19:16

score 206 · Answer 8 · 2026-04-15 12:38:28

206

Views

Description of ideals of ring $F[x]/(x^n)$?

Published on 15 Apr 2026 - 12:38

score 925 · Answer 9 · 2026-04-03 23:06:00

925

Views

$p$ is a positive integer and $(p)$ is a maximal ideal in the ring $(\mathbb Z, +,\cdot)$, then $p$ is a prime number

Published on 03 Apr 2026 - 23:06

score 63 · Answer 10 · 2026-04-13 06:49:31

63

Views

Height of $p/a$ is less or equal than the height of $p$.

Published on 13 Apr 2026 - 6:49

score 394 · Answer 11 · 2026-03-27 02:39:40

394

Views

$R$ semisimple artinian ring $\Rightarrow\varphi(R)$ is such

Published on 27 Mar 2026 - 2:39

score 626 · Answer 12 · 2026-04-14 08:53:59

626

Views

Augmentation ideal and the abelianization of $G$

Published on 14 Apr 2026 - 8:53

score 368 · Answer 13 · 2026-04-12 23:05:11

368

Views

Shortcut to: the radical of a proper ideal $I$ is the intersection of all prime ideals $\supset I$.

Published on 12 Apr 2026 - 23:05

score 572 · Answer 14 · 2026-04-14 01:13:29

572

Views

If $Q$ is an ideal whose radical is a maximal ideal, then $Q$ is a primary ideal.

Published on 14 Apr 2026 - 1:13

score 130 · Answer 15 · 2026-04-14 09:54:42

130

Views

Why is this sequence of ideals an ascending chain? In proof of irreducible ideals are primary.

Published on 14 Apr 2026 - 9:54

List Question

Is $\mathbb{Z}[x]\over \langle x+3\rangle$ field?

If $JA_{P}\subset IA_{ P}$ for every associated prime, then $J\subset I$

Any left ideal of $M_n(\mathbb{F})$ is principal

Determining the structure of the quotient ring $\mathbb{Z}[x]/(x^2+3,p)$

Prove that $f:I\oplus J\to R\oplus IJ: (i,j)\mapsto (i+j,ij_0-i_0j)$ is surjective for coprime $I,J$

For $\mathfrak{m}$ maximal and principal, there's no ideal between $\mathfrak{m}^2$ and $\mathfrak{m}$

an example of a non convex ideal

Description of ideals of ring $F[x]/(x^n)$?

$p$ is a positive integer and $(p)$ is a maximal ideal in the ring $(\mathbb Z, +,\cdot)$, then $p$ is a prime number

Height of $p/a$ is less or equal than the height of $p$.

$R$ semisimple artinian ring $\Rightarrow\varphi(R)$ is such

Augmentation ideal and the abelianization of $G$

Shortcut to: the radical of a proper ideal $I$ is the intersection of all prime ideals $\supset I$.

If $Q$ is an ideal whose radical is a maximal ideal, then $Q$ is a primary ideal.

Why is this sequence of ideals an ascending chain? In proof of irreducible ideals are primary.

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