Question

Every element in a ring with finitely many ideals is either a unit or a zero divisor.

score 1.1k · Answer 1 · 2026-04-24 22:50:16

1.1k

Views

Every element in a ring with finitely many ideals is either a unit or a zero divisor.

Published on 24 Apr 2026 - 22:50

score 63 · Answer 2 · 2026-04-15 19:17:18

63

Views

Let $R=\mathbb{Z}/2[x]$ and $I=R(x^{17}-1)$. Is there a nonzero element $y$ of $R/I$ with $y^2=0$?

Published on 15 Apr 2026 - 19:17

score 1.6k · Answer 3 · 2026-04-17 06:25:36

1.6k

Views

Find all roots of $\,x^2\!\equiv x\pmod{\!900}$, i.e all idempotents in $\Bbb Z_{900}$

Published on 17 Apr 2026 - 6:25

score 453 · Answer 4 · 2026-04-24 22:49:54

453

Views

Proof that presheaf is a sheaf for Spec

Published on 24 Apr 2026 - 22:49

score 1k · Answer 5 · 2026-04-12 06:43:28

1k

Views

A number system that is not unique factorization domain

Published on 12 Apr 2026 - 6:43

score 2.6k · Answer 6 · 2026-04-14 13:42:04

2.6k

Views

Is division allowed in rings and fields?

Published on 14 Apr 2026 - 13:42

score 102 · Answer 7 · 2026-04-16 12:54:23

102

Views

Every prime ideal is max. if anysequence $I_1 \supseteq I_2 \supseteq I_3 \supseteq \cdots $ stabilises?

Published on 16 Apr 2026 - 12:54

score 99 · Answer 8 · 2026-04-14 11:35:36

99

Views

Showing the existence of sub fields of a finite field

Published on 14 Apr 2026 - 11:35

score 3.9k · Answer 9 · 2026-04-11 06:20:00

3.9k

Views

Integral ring extensions and finitely generated as a module

Published on 11 Apr 2026 - 6:20

score 124 · Answer 10 · 2026-04-11 06:20:20

124

Views

A non-UFD such that $a^2 \mid b^2$ does not lead to $a\mid b$

Published on 11 Apr 2026 - 6:20

score 323 · Answer 11 · 2026-04-13 05:34:02

323

Views

Converting a polynomial ring to a numerical ring (transport of structure)

Published on 13 Apr 2026 - 5:34

score 51 · Answer 12 · 2026-04-15 11:08:35

51

Views

Non-UFD that there exists set $X$ of any cardinality and $a$ that $xy$ is not divisible by $a^2$ for any $x,y \in X$ and $x^2$ is divisible by $a^2$

Published on 15 Apr 2026 - 11:08

score 614 · Answer 13 · 2026-04-12 13:10:39

614

Views

Ideal quotient and extension

Published on 12 Apr 2026 - 13:10

score 66 · Answer 14 · 2026-04-14 06:50:21

66

Views

Rapid and easy question on ideals and ring

Published on 14 Apr 2026 - 6:50

score 2.6k · Answer 15 · 2026-04-16 00:57:00

2.6k

Views

Relating the characteristic of the ring R to the characteristic of R[x]

Published on 16 Apr 2026 - 0:57

List Question

Every element in a ring with finitely many ideals is either a unit or a zero divisor.

Let $R=\mathbb{Z}/2[x]$ and $I=R(x^{17}-1)$. Is there a nonzero element $y$ of $R/I$ with $y^2=0$?

Find all roots of $\,x^2\!\equiv x\pmod{\!900}$, i.e all idempotents in $\Bbb Z_{900}$

Proof that presheaf is a sheaf for Spec

A number system that is not unique factorization domain

Is division allowed in rings and fields?

Every prime ideal is max. if anysequence $I_1 \supseteq I_2 \supseteq I_3 \supseteq \cdots $ stabilises?

Showing the existence of sub fields of a finite field

Integral ring extensions and finitely generated as a module

A non-UFD such that $a^2 \mid b^2$ does not lead to $a\mid b$

Converting a polynomial ring to a numerical ring (transport of structure)

Non-UFD that there exists set $X$ of any cardinality and $a$ that $xy$ is not divisible by $a^2$ for any $x,y \in X$ and $x^2$ is divisible by $a^2$

Ideal quotient and extension

Rapid and easy question on ideals and ring

Relating the characteristic of the ring R to the characteristic of R[x]

Trending Questions

Popular # Hahtags

Popular Questions