Question

Definition for a distance function over a residue class ring

score 61 · Answer 1 · 2014-06-21 18:33:03

61

Views

Definition for a distance function over a residue class ring

Published on 21 Jun 2014 - 18:33

score 1.6k · Answer 2 · 2014-06-24 04:39:09

1.6k

Views

Basis of the localization of a free module is the localization of its basis?

Published on 24 Jun 2014 - 4:39

score 130 · Answer 3 · 2026-03-25 09:27:39

130

Views

Is $R[X]/(f)$ Cohen-Macaulay if $R$ is so?

Published on 25 Mar 2026 - 9:27

score 75 · Answer 4 · 2014-06-24 17:18:04

75

Views

Expressing $\mathcal O_L$ as a certain free module of rank 1

Published on 24 Jun 2014 - 17:18

score 77 · Answer 5 · 2026-03-25 15:55:48

77

Views

Show that if $R$ is principal, $N $ is pure and $Ann(x+N)= Rd$ then there exists $y \in M$ such that $x+N=y+N$ and $Ann(y)=Rd$

Published on 25 Mar 2026 - 15:55

score 41 · Answer 6 · 2014-06-25 13:37:00

41

Views

$x\in{\rm span}(S\cup\{y\}), x\notin{\rm span}(S)$ implies $y\in{\rm span}(S\cup\{x\})$

Published on 25 Jun 2014 - 13:37

score 85 · Answer 7 · 2014-06-25 21:44:34

85

Views

Smoothness and field of fractions

Published on 25 Jun 2014 - 21:44

score 1.2k · Answer 8 · 2014-06-26 13:42:10

1.2k

Views

Modules over local artinian rings

Published on 26 Jun 2014 - 13:42

score 935 · Answer 9 · 2026-03-28 10:35:25

935

Views

Commutativity of direct and inverse limits

Published on 28 Mar 2026 - 10:35

score 2k · Answer 10 · 2026-03-28 10:16:13

2k

Views

Defining algebras over noncommutative rings

Published on 28 Mar 2026 - 10:16

score 245 · Answer 11 · 2026-03-27 23:57:39

245

Views

Smith normal forms and a math program

Published on 27 Mar 2026 - 23:57

score 696 · Answer 12 · 2026-03-25 23:19:57

696

Views

Conditions for a quotient module to be Noetherian

Published on 25 Mar 2026 - 23:19

score 873 · Answer 13 · 2014-06-29 12:07:37

873

Views

If $\{M_i\}_{i \in I}$ is a family of $R$-modules free, then the product $\prod_{i \in I}M_i$ is free?

Published on 29 Jun 2014 - 12:07

score 319 · Answer 14 · 2014-06-29 14:24:53

319

Views

In a semi-simple module, any submodule is a direct factor?

Published on 29 Jun 2014 - 14:24

score 1k · Answer 15 · 2014-06-29 17:41:42

1k

Views

A finite module over a Noetherian ring is torsionless if and only if it is a submodule of a finite free module

Published on 29 Jun 2014 - 17:41

List Question

Definition for a distance function over a residue class ring

Basis of the localization of a free module is the localization of its basis?

Is $R[X]/(f)$ Cohen-Macaulay if $R$ is so?

Expressing $\mathcal O_L$ as a certain free module of rank 1

Show that if $R$ is principal, $N $ is pure and $Ann(x+N)= Rd$ then there exists $y \in M$ such that $x+N=y+N$ and $Ann(y)=Rd$

$x\in{\rm span}(S\cup\{y\}), x\notin{\rm span}(S)$ implies $y\in{\rm span}(S\cup\{x\})$

Smoothness and field of fractions

Modules over local artinian rings

Commutativity of direct and inverse limits

Defining algebras over noncommutative rings

Smith normal forms and a math program

Conditions for a quotient module to be Noetherian

If $\{M_i\}_{i \in I}$ is a family of $R$-modules free, then the product $\prod_{i \in I}M_i$ is free?

In a semi-simple module, any submodule is a direct factor?

A finite module over a Noetherian ring is torsionless if and only if it is a submodule of a finite free module

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