Question

Are the invertible matrices which are used to find the SNF always part of the ideal principle domain?

score 21 · Answer 1 · 2026-02-23 08:07:02

21

Views

Are the invertible matrices which are used to find the SNF always part of the ideal principle domain?

Published on 23 Feb 2026 - 8:07

score 25 · Answer 2 · 2026-02-23 08:05:04

25

Views

What is meant by "invertible" matrices in the creation of a SNM

Published on 23 Feb 2026 - 8:05

score 97 · Answer 3 · 2026-03-28 08:35:33

97

Views

Exhibit all the ideals in the ring $F[x]/(p(x))$, where $F$ is a field and $p(x)∈F[x]$ (describe them in terms of the factorization of $p(x)$)

Published on 28 Mar 2026 - 8:35

score 51 · Answer 4 · 2026-03-29 03:03:38

51

Views

If every irreducible elements in Noetherian ring is prime, it is UFD

Published on 29 Mar 2026 - 3:03

score 72 · Answer 5 · 2023-11-22 18:53:58

72

Views

Primary component of a finitely generated module over PID is a direct sum of cyclic modules.

Published on 22 Nov 2023 - 18:53

score 129 · Answer 6 · 2023-11-23 18:21:39

129

Views

Pure submodule that is a direct summand

Published on 23 Nov 2023 - 18:21

score 54 · Answer 7 · 2026-03-26 22:52:30

54

Views

Free submodules of an integral $R.$

Published on 26 Mar 2026 - 22:52

score 30 · Answer 8 · 2023-12-10 19:47:18

30

Views

Deduce Jordan Normal Form from PID finitely generated module structure.

Published on 10 Dec 2023 - 19:47

score 65 · Answer 9 · 2026-03-26 16:08:50

65

Views

$\mathbb Z[\xi_{2n}]$ is a pid

Published on 26 Mar 2026 - 16:08

score 62 · Answer 10 · 2026-03-29 03:36:44

62

Views

Let R be a UFD such that each maximal ideal of R is a principal ideal, prove that R is a PID

Published on 29 Mar 2026 - 3:36

score 144 · Answer 11 · 2026-03-27 05:39:03

144

Views

Need help showing that the only submodules of $M$ are the ones in an ascending chain.

Published on 27 Mar 2026 - 5:39

score 42 · Answer 12 · 2023-12-25 20:45:59

42

Views

$ (x-a_1) \cap \ldots \cap (x-a_n) = (p) $ in $ \mathbb{C}[x]$ reasoning

Published on 25 Dec 2023 - 20:45

score 109 · Answer 13 · 2026-03-25 15:38:16

109

Views

A case where submodules, isomorphic as modules, are isomorphic as submodules

Published on 25 Mar 2026 - 15:38

score 31 · Answer 14 · 2024-01-08 14:57:40

31

Views

Trying to define Dedekind-Hasse norm in a PID

Published on 08 Jan 2024 - 14:57

score 47 · Answer 15 · 2024-01-14 00:28:18

47

Views

The multiplicative group of a finite field is cyclic, using modules

Published on 14 Jan 2024 - 0:28

List Question

Are the invertible matrices which are used to find the SNF always part of the ideal principle domain?

What is meant by "invertible" matrices in the creation of a SNM

Exhibit all the ideals in the ring $F[x]/(p(x))$, where $F$ is a field and $p(x)∈F[x]$ (describe them in terms of the factorization of $p(x)$)

If every irreducible elements in Noetherian ring is prime, it is UFD

Primary component of a finitely generated module over PID is a direct sum of cyclic modules.

Pure submodule that is a direct summand

Free submodules of an integral $R.$

Deduce Jordan Normal Form from PID finitely generated module structure.

$\mathbb Z[\xi_{2n}]$ is a pid

Let R be a UFD such that each maximal ideal of R is a principal ideal, prove that R is a PID

Need help showing that the only submodules of $M$ are the ones in an ascending chain.

$ (x-a_1) \cap \ldots \cap (x-a_n) = (p) $ in $ \mathbb{C}[x]$ reasoning

A case where submodules, isomorphic as modules, are isomorphic as submodules

Trying to define Dedekind-Hasse norm in a PID

The multiplicative group of a finite field is cyclic, using modules

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