Question

Finding essential ideal in a ring $R$

score 251 · Answer 1 · 2018-12-21 11:49:35

251

Views

Finding essential ideal in a ring $R$

Published on 21 Dec 2018 - 11:49

score 333 · Answer 2 · 2026-03-28 21:06:30

333

Views

Determine the maximal ideals of $\mathbb R^2$ by noting $\mathbb R^2 \cong \mathbb R[x]/(x^2-1)$

Published on 28 Mar 2026 - 21:06

score 1.6k · Answer 3 · 2026-03-25 16:01:16

1.6k

Views

Determine maximal ideals of $\mathbb R[x]/(x^2)$

Published on 25 Mar 2026 - 16:01

score 677 · Answer 4 · 2026-03-26 07:35:37

677

Views

A real polynomial of degree more than or equal to 3 is reducible, but does it necessarily have a real zero?

Published on 26 Mar 2026 - 7:35

score 2.2k · Answer 5 · 2026-03-25 05:07:38

2.2k

Views

If ideal $I$ of domain $R$ is free $R$-module, then $I$ is principal ideal.

Published on 25 Mar 2026 - 5:07

score 354 · Answer 6 · 2018-12-22 15:53:18

354

Views

When a polynomial quotient algebra is semi-simple

Published on 22 Dec 2018 - 15:53

score 94 · Answer 7 · 2026-03-25 03:02:34

94

Views

The correspondence between maximal ideals in an algebra and it's unitalization

Published on 25 Mar 2026 - 3:02

score 209 · Answer 8 · 2018-12-23 17:15:15

209

Views

If $I,J,K$ are ideals of a ring $R$ and $I+J=J+K=K+I=R$ then $IJ+JK+KI=R$

Published on 23 Dec 2018 - 17:15

score 1.5k · Answer 9 · 2018-12-24 03:36:10

1.5k

Views

If I and J are two ideals, I∪J is an ideal if and only if I⊂J or J⊂I. How can we prove the subset part?

Published on 24 Dec 2018 - 3:36

score 108 · Answer 10 · 2018-12-25 20:35:43

108

Views

$f(x)$ is irreducible polynomial on field $k$, $f(\alpha)=0$. $k'$ is field extension of $k$, then $k(\alpha)\otimes_kk'\cong k'[x]/(f(x))$

Published on 25 Dec 2018 - 20:35

score 389 · Answer 11 · 2026-03-28 15:26:07

389

Views

Determine the maximal ideals of $\mathbb R^2$ by determining all its ideals.

Published on 28 Mar 2026 - 15:26

score 101 · Answer 12 · 2018-12-29 20:00:54

101

Views

Using the Minkowski Bound

Published on 29 Dec 2018 - 20:00

score 230 · Answer 13 · 2026-03-25 02:57:31

230

Views

Commutative local ring with $10$ ideals

Published on 25 Mar 2026 - 2:57

score 600 · Answer 14 · 2018-12-30 10:29:46

600

Views

ring in which every proper ideal is primary

Published on 30 Dec 2018 - 10:29

score 109 · Answer 15 · 2026-03-27 19:40:05

109

Views

Prove two Ideal are equal

Published on 27 Mar 2026 - 19:40

List Question

Finding essential ideal in a ring $R$

Determine the maximal ideals of $\mathbb R^2$ by noting $\mathbb R^2 \cong \mathbb R[x]/(x^2-1)$

Determine maximal ideals of $\mathbb R[x]/(x^2)$

A real polynomial of degree more than or equal to 3 is reducible, but does it necessarily have a real zero?

If ideal $I$ of domain $R$ is free $R$-module, then $I$ is principal ideal.

When a polynomial quotient algebra is semi-simple

The correspondence between maximal ideals in an algebra and it's unitalization

If $I,J,K$ are ideals of a ring $R$ and $I+J=J+K=K+I=R$ then $IJ+JK+KI=R$

If I and J are two ideals, I∪J is an ideal if and only if I⊂J or J⊂I. How can we prove the subset part?

$f(x)$ is irreducible polynomial on field $k$, $f(\alpha)=0$. $k'$ is field extension of $k$, then $k(\alpha)\otimes_kk'\cong k'[x]/(f(x))$

Determine the maximal ideals of $\mathbb R^2$ by determining all its ideals.

Using the Minkowski Bound

Commutative local ring with $10$ ideals

ring in which every proper ideal is primary

Prove two Ideal are equal

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