Question

If any "dividing" chain "terminates" at some point, does that imply an integral domain being P.I.D.?

score 64 · Answer 1 · 2021-12-30 07:45:52

64

Views

If any "dividing" chain "terminates" at some point, does that imply an integral domain being P.I.D.?

Published on 30 Dec 2021 - 7:45

score 77 · Answer 2 · 2021-12-30 12:11:14

77

Views

Showing that $x+x^2$ belongs to an ideal in $\mathbb{Z}_2[x]$

Published on 30 Dec 2021 - 12:11

score 43 · Answer 3 · 2026-03-29 10:08:48

43

Views

Let $D$ be an integral domain and let $c\in D$ be irreducible in $D$. Show the ideal $(x,c)$ in $D[x]$ is not principal.

Published on 29 Mar 2026 - 10:08

score 111 · Answer 4 · 2026-03-25 23:36:01

111

Views

$\mathbb{Z}[i]$-modules with 101 elements and cyclic $\mathbb{Z}[i]$-torsion modules

Published on 25 Mar 2026 - 23:36

score 165 · Answer 5 · 2026-03-29 11:44:26

165

Views

Ideal of Polynomial Function on a Circle that Vanish at a Point

Published on 29 Mar 2026 - 11:44

score 37 · Answer 6 · 2026-03-27 09:15:31

37

Views

Linear transformations over PIDs/ EDs

Published on 27 Mar 2026 - 9:15

score 281 · Answer 7 · 2026-03-27 10:38:54

281

Views

Why does this proof generalize for all norms? $\mathbb Z[\sqrt{-5}]$ is not an Euclidean Domain.

Published on 27 Mar 2026 - 10:38

score 126 · Answer 8 · 2026-03-29 21:11:19

126

Views

If $N \leq M$, there exist free modules $F_N \leq N$, $F_M \leq M$ with $N = F_N \oplus N_{tor}$, $M = F_M \oplus M_{tor}$ with $F_N \leq F_M$

Published on 29 Mar 2026 - 21:11

score 164 · Answer 9 · 2022-01-30 15:05:04

164

Views

Bounds involving number of invariant factors and elementary divisors

Published on 30 Jan 2022 - 15:05

score 50 · Answer 10 · 2026-03-30 10:55:58

50

Views

Equivalent condition for uniserial torsion module over a PID

Published on 30 Mar 2026 - 10:55

score 28 · Answer 11 · 2022-02-09 12:46:51

28

Views

Content of a polynomial and maximal ideals.

Published on 09 Feb 2022 - 12:46

score 31 · Answer 12 · 2022-02-09 13:31:32

31

Views

How does this quotient by a maximal ideal looks like?

Published on 09 Feb 2022 - 13:31

score 91 · Answer 13 · 2022-02-13 15:54:12

91

Views

Terminology for invariant factors of quotient module over PID

Published on 13 Feb 2022 - 15:54

score 93 · Answer 14 · 2022-02-17 11:30:12

93

Views

Question regarding divisibility of invariant factors in Smith Normal Form.

Published on 17 Feb 2022 - 11:30

score 80 · Answer 15 · 2022-02-26 04:24:17

80

Views

Is PID with one divisible element a field?

Published on 26 Feb 2022 - 4:24

List Question

If any "dividing" chain "terminates" at some point, does that imply an integral domain being P.I.D.?

Showing that $x+x^2$ belongs to an ideal in $\mathbb{Z}_2[x]$

Let $D$ be an integral domain and let $c\in D$ be irreducible in $D$. Show the ideal $(x,c)$ in $D[x]$ is not principal.

$\mathbb{Z}[i]$-modules with 101 elements and cyclic $\mathbb{Z}[i]$-torsion modules

Ideal of Polynomial Function on a Circle that Vanish at a Point

Linear transformations over PIDs/ EDs

Why does this proof generalize for all norms? $\mathbb Z[\sqrt{-5}]$ is not an Euclidean Domain.

If $N \leq M$, there exist free modules $F_N \leq N$, $F_M \leq M$ with $N = F_N \oplus N_{tor}$, $M = F_M \oplus M_{tor}$ with $F_N \leq F_M$

Bounds involving number of invariant factors and elementary divisors

Equivalent condition for uniserial torsion module over a PID

Content of a polynomial and maximal ideals.

How does this quotient by a maximal ideal looks like?

Terminology for invariant factors of quotient module over PID

Question regarding divisibility of invariant factors in Smith Normal Form.

Is PID with one divisible element a field?

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