Question

What is $[O_{L}:O]$ and $[O_{L}/(\pi):O/(\pi)]$?

score 69 · Answer 1 · 2026-05-01 21:11:39

69

Views

What is $[O_{L}:O]$ and $[O_{L}/(\pi):O/(\pi)]$?

Published on 01 May 2026 - 21:11

score 114 · Answer 2 · 2026-05-10 13:09:44

114

Views

Characterization of trivial localization of module?

Published on 10 May 2026 - 13:09

score 333 · Answer 3 · 2026-04-17 04:18:25

333

Views

Are module categories over a semisimple category semisimple?

Published on 17 Apr 2026 - 4:18

score 460 · Answer 4 · 2026-04-15 14:23:02

460

Views

Homomorphism of $k[x]$-modules

Published on 15 Apr 2026 - 14:23

score 247 · Answer 5 · 2026-04-29 12:42:49

247

Views

torsion-free modules $M$ over Noetherian domain of dimension $1$ for which $l(M/aM) \le (\dim_K K \otimes_R M) \cdot l(R/aR), \forall 0 \ne a \in R$

Published on 29 Apr 2026 - 12:42

score 63 · Answer 6 · 2026-04-14 11:28:28

63

Views

Show that cardinality of $\mathbb{Z}^n/T(\mathbb{Z}^n)$ equals the absolute value of the determinant of the matrix representing the homomorphism T

Published on 14 Apr 2026 - 11:28

score 324 · Answer 7 · 2026-05-10 15:11:47

324

Views

Prove that for each submodule $B$, there exist a submodule $C$ such that $A=B\oplus C$.

Published on 10 May 2026 - 15:11

score 19 · Answer 8 · 2026-04-12 09:54:17

19

Views

Proof of right module over the ring $M_{2}(\mathbb{Z})$

Published on 12 Apr 2026 - 9:54

score 585 · Answer 9 · 2026-04-29 12:42:29

585

Views

Why is a Nonzero Ideal of $\mathcal{O}_K$ Free of Rank $n$?

Published on 29 Apr 2026 - 12:42

score 202 · Answer 10 · 2026-05-03 07:32:36

202

Views

Checking if quotient ring is Noetherian or Artinian over a module

Published on 03 May 2026 - 7:32

score 54 · Answer 11 · 2026-04-10 20:32:49

54

Views

solving linear equation with modulus

Published on 10 Apr 2026 - 20:32

score 298 · Answer 12 · 2026-04-30 02:41:01

298

Views

Modules over $k[x]$

Published on 30 Apr 2026 - 2:41

score 127 · Answer 13 · 2026-04-12 00:00:53

127

Views

If $C = A \oplus B$ then $A \cong C/B$.

Published on 12 Apr 2026 - 0:00

score 334 · Answer 14 · 2026-05-07 11:28:07

334

Views

Structure theorem for modules implies Smith Normal Form

Published on 07 May 2026 - 11:28

score 890 · Answer 15 · 2026-05-07 10:08:12

890

Views

Let R be a PID, B a torsion R module and p a prime in R. Prove that if $pb=0$ for some non zero b in B, then $\text{Ann}(B)$ is a subset of (p)

Published on 07 May 2026 - 10:08

List Question

What is $[O_{L}:O]$ and $[O_{L}/(\pi):O/(\pi)]$?

Characterization of trivial localization of module?

Are module categories over a semisimple category semisimple?

Homomorphism of $k[x]$-modules

torsion-free modules $M$ over Noetherian domain of dimension $1$ for which $l(M/aM) \le (\dim_K K \otimes_R M) \cdot l(R/aR), \forall 0 \ne a \in R$

Show that cardinality of $\mathbb{Z}^n/T(\mathbb{Z}^n)$ equals the absolute value of the determinant of the matrix representing the homomorphism T

Prove that for each submodule $B$, there exist a submodule $C$ such that $A=B\oplus C$.

Proof of right module over the ring $M_{2}(\mathbb{Z})$

Why is a Nonzero Ideal of $\mathcal{O}_K$ Free of Rank $n$?

Checking if quotient ring is Noetherian or Artinian over a module

solving linear equation with modulus

Modules over $k[x]$

If $C = A \oplus B$ then $A \cong C/B$.

Structure theorem for modules implies Smith Normal Form

Let R be a PID, B a torsion R module and p a prime in R. Prove that if $pb=0$ for some non zero b in B, then $\text{Ann}(B)$ is a subset of (p)

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