Question

Show that if $M$ is a R-module free, for all $r \in R$ and $m \in M$ such that $r \neq 0$ e $m \neq 0$ we have $rm \neq 0$.

score 55 · Answer 1 · 2026-04-15 14:43:47

55

Views

Show that if $M$ is a R-module free, for all $r \in R$ and $m \in M$ such that $r \neq 0$ e $m \neq 0$ we have $rm \neq 0$.

Published on 15 Apr 2026 - 14:43

score 3.9k · Answer 2 · 2026-04-13 08:32:04

3.9k

Views

Rings with noncommutative addition

Published on 13 Apr 2026 - 8:32

score 2.1k · Answer 3 · 2026-04-23 10:44:27

2.1k

Views

Finitely many prime ideals $\Rightarrow$ cartesian product of local rings

Published on 23 Apr 2026 - 10:44

score 165 · Answer 4 · 2026-04-16 13:22:39

165

Views

Is the ring $ R = \{ f \in \mathbb{C}[x,y] \mid {\nabla f}(0,0) = (0,0) \} $ Noetherian?

Published on 16 Apr 2026 - 13:22

score 496 · Answer 5 · 2026-04-15 14:33:32

496

Views

Ring homomorphisms map non units to non units

Published on 15 Apr 2026 - 14:33

score 278 · Answer 6 · 2026-04-12 11:12:55

278

Views

Height of finitely generated ideals in a catenary local ring

Published on 12 Apr 2026 - 11:12

score 3k · Answer 7 · 2026-04-12 05:30:12

3k

Views

When a monomial ideal is primary

Published on 12 Apr 2026 - 5:30

score 1.7k · Answer 8 · 2026-04-23 10:19:01

1.7k

Views

About second uniqueness primary decomposition theorem

Published on 23 Apr 2026 - 10:19

score 103 · Answer 9 · 2026-04-23 10:43:30

103

Views

Show that $f^{-1}(\langle0\rangle)$ is not a maximal ideal of $\mathbb{Z}$.

Published on 23 Apr 2026 - 10:43

score 468 · Answer 10 · 2026-04-17 05:30:26

468

Views

Questions about $\Bbb Q[\sqrt{p}]$ and $\Bbb Q(\sqrt{p})$

Published on 17 Apr 2026 - 5:30

score 366 · Answer 11 · 2026-04-15 11:19:47

366

Views

If $p$ is an irreducible element of an integral domain $D$, and if $e$ belongs to $D^\ast$ prove that $ep$ is also ireducible

Published on 15 Apr 2026 - 11:19

score 710 · Answer 12 · 2026-04-15 01:35:54

710

Views

Prove that $6$ and $2(1+\sqrt{-5})$ do not have a gcd in $\mathbb{Z}[\sqrt{-5}]$

Published on 15 Apr 2026 - 1:35

score 381 · Answer 13 · 2026-04-23 15:08:06

381

Views

Pseudo associated primes and short exact sequences

Published on 23 Apr 2026 - 15:08

score 169 · Answer 14 · 2026-04-16 05:03:04

169

Views

Rings which are finitely generated and free over Cohen-Macaulay rings are also Cohen-Macaulay

Published on 16 Apr 2026 - 5:03

score 86 · Answer 15 · 2026-04-23 15:19:07

86

Views

Canonical homomorphisms $R_{\mathfrak{p}_i} \to R/\mathfrak{p}_i^n$ are isomorphisms when $R$ is artinian

Published on 23 Apr 2026 - 15:19

List Question

Show that if $M$ is a R-module free, for all $r \in R$ and $m \in M$ such that $r \neq 0$ e $m \neq 0$ we have $rm \neq 0$.

Rings with noncommutative addition

Finitely many prime ideals $\Rightarrow$ cartesian product of local rings

Is the ring $ R = \{ f \in \mathbb{C}[x,y] \mid {\nabla f}(0,0) = (0,0) \} $ Noetherian?

Ring homomorphisms map non units to non units

Height of finitely generated ideals in a catenary local ring

When a monomial ideal is primary

About second uniqueness primary decomposition theorem

Show that $f^{-1}(\langle0\rangle)$ is not a maximal ideal of $\mathbb{Z}$.

Questions about $\Bbb Q[\sqrt{p}]$ and $\Bbb Q(\sqrt{p})$

If $p$ is an irreducible element of an integral domain $D$, and if $e$ belongs to $D^\ast$ prove that $ep$ is also ireducible

Prove that $6$ and $2(1+\sqrt{-5})$ do not have a gcd in $\mathbb{Z}[\sqrt{-5}]$

Pseudo associated primes and short exact sequences

Rings which are finitely generated and free over Cohen-Macaulay rings are also Cohen-Macaulay

Canonical homomorphisms $R_{\mathfrak{p}_i} \to R/\mathfrak{p}_i^n$ are isomorphisms when $R$ is artinian

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