Question

Definition of principal ideal in rings

score 38 · Answer 1 · 2026-03-31 05:12:44

38

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Definition of principal ideal in rings

Published on 31 Mar 2026 - 5:12

score 59 · Answer 2 · 2026-03-25 09:28:33

59

Views

By showing that $R/I$ is an integral domain, deduce that it's a field.

Published on 25 Mar 2026 - 9:28

score 54 · Answer 3 · 2026-04-02 11:21:24

If $I\subseteq R$ is a uniserial ideal of $R$ with finite length and $R/I$ is uniserial of finite length, then $R$ is uniserial of finite length

score 680 · Answer 4 · 2026-03-25 16:02:19

680

Views

Prove that there is a unique homomorphism from $\mathbb{Z} [i]$ to $\mathbb{Z}/2\mathbb{Z}$.

Published on 25 Mar 2026 - 16:02

score 335 · Answer 5 · 2026-04-02 11:09:45

335

Views

Isomorphic $\mathbb{C}[X]$-modules

Published on 02 Apr 2026 - 11:09

score 310 · Answer 6 · 2026-03-31 17:01:23

310

Views

Find the Addition and Multiplication tables for GF(7)

Published on 31 Mar 2026 - 17:01

score 473 · Answer 7 · 2026-03-25 15:48:36

473

Views

Artin-wedderburn and simple modules

Published on 25 Mar 2026 - 15:48

score 687 · Answer 8 · 2026-03-31 05:25:33

687

Views

If $A$ and $B$ are ideals of a ring $R$. Then $A+B$ is an ideal of $R$ generated by $A \cup B$?

Published on 31 Mar 2026 - 5:25

score 71 · Answer 9 · 2026-03-27 01:53:38

71

Views

Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible

Published on 27 Mar 2026 - 1:53

score 119 · Answer 10 · 2026-03-31 05:18:31

119

Views

Finding elements of the principal ideal $(10)$.

Published on 31 Mar 2026 - 5:18

score 59 · Answer 11 · 2026-03-31 05:17:33

59

Views

Describing elements in a principal ideal in a ring that does not have a $1$.

Published on 31 Mar 2026 - 5:17

score 79 · Answer 12 · 2019-05-06 11:59:16

79

Views

Construction of rings $(R^n,+,\times)$, given a ring $(R,+,\times)$ and a natural $n\ge 2$.

Published on 06 May 2019 - 11:59

score 66 · Answer 13 · 2026-04-02 11:14:41

66

Views

Proof that $\Omega_{S^{-1}B/A}=S^{-1}\Omega_{B/A}$

Published on 02 Apr 2026 - 11:14

score 261 · Answer 14 · 2019-05-06 16:23:51

261

Views

If $S$ is a quotient ring of $R$, then either $char(S)$ divides $char(R)$, or $char(S)=0$

Published on 06 May 2019 - 16:23

score 165 · Answer 15 · 2026-03-25 11:01:42

165

Views

How do I find the generator $(g)$ that generates $(29, \sqrt{-5} ± 13)$

Published on 25 Mar 2026 - 11:01

List Question

Definition of principal ideal in rings

By showing that $R/I$ is an integral domain, deduce that it's a field.

If $I\subseteq R$ is a uniserial ideal of $R$ with finite length and $R/I$ is uniserial of finite length, then $R$ is uniserial of finite length

Prove that there is a unique homomorphism from $\mathbb{Z} [i]$ to $\mathbb{Z}/2\mathbb{Z}$.

Isomorphic $\mathbb{C}[X]$-modules

Find the Addition and Multiplication tables for GF(7)

Artin-wedderburn and simple modules

If $A$ and $B$ are ideals of a ring $R$. Then $A+B$ is an ideal of $R$ generated by $A \cup B$?

Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible

Finding elements of the principal ideal $(10)$.

Describing elements in a principal ideal in a ring that does not have a $1$.

Construction of rings $(R^n,+,\times)$, given a ring $(R,+,\times)$ and a natural $n\ge 2$.

Proof that $\Omega_{S^{-1}B/A}=S^{-1}\Omega_{B/A}$

If $S$ is a quotient ring of $R$, then either $char(S)$ divides $char(R)$, or $char(S)=0$

How do I find the generator $(g)$ that generates $(29, \sqrt{-5} ± 13)$

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