Question

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

score 58 · Answer 1 · 2026-03-20 02:42:07

58

Views

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

Published on 20 Mar 2026 - 2:42

score 110 · Answer 2 · 2026-03-17 10:17:10

110

Views

Characterization of trivial localization of module?

Published on 17 Mar 2026 - 10:17

score 331 · Answer 3 · 2026-03-25 09:50:49

331

Views

Are module categories over a semisimple category semisimple?

Published on 25 Mar 2026 - 9:50

score 457 · Answer 4 · 2018-02-14 16:01:16

457

Views

Homomorphism of $k[x]$-modules

Published on 14 Feb 2018 - 16:01

score 239 · Answer 5 · 2026-03-23 03:17:17

239

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 23 Mar 2026 - 3:17

score 60 · Answer 6 · 2018-02-15 11:05:32

60

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 15 Feb 2018 - 11:05

score 317 · Answer 7 · 2026-03-22 16:47:14

317

Views

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

Published on 22 Mar 2026 - 16:47

score 17 · Answer 8 · 2026-03-17 00:57:53

17

Views

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

Published on 17 Mar 2026 - 0:57

score 575 · Answer 9 · 2026-03-25 05:21:00

575

Views

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

Published on 25 Mar 2026 - 5:21

score 195 · Answer 10 · 2026-03-22 17:24:19

195

Views

Checking if quotient ring is Noetherian or Artinian over a module

Published on 22 Mar 2026 - 17:24

score 51 · Answer 11 · 2018-02-17 13:23:33

51

Views

solving linear equation with modulus

Published on 17 Feb 2018 - 13:23

score 293 · Answer 12 · 2018-02-18 16:39:23

293

Views

Modules over $k[x]$

Published on 18 Feb 2018 - 16:39

score 124 · Answer 13 · 2018-02-19 21:11:36

124

Views

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

Published on 19 Feb 2018 - 21:11

score 325 · Answer 14 · 2026-03-20 08:04:43

325

Views

Structure theorem for modules implies Smith Normal Form

Published on 20 Mar 2026 - 8:04

score 882 · Answer 15 · 2026-03-20 08:37:52

882

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 20 Mar 2026 - 8:37

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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