Question

Let $A=\mathbb Q[x_1,...,x_n]$ and let $M$ be an $A$-module. Show that $l_A(M)$ is finite if and only if $\dim_{\mathbb Q}(M)$ is finite.

score 98 · Answer 1 · 2026-04-16 20:33:49

Let $A=\mathbb Q[x_1,...,x_n]$ and let $M$ be an $A$-module. Show that $l_A(M)$ is finite if and only if $\dim_{\mathbb Q}(M)$ is finite.

score 111 · Answer 2 · 2026-04-14 23:01:48

111

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score 62 · Answer 3 · 2026-04-09 05:34:35

62

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score 55 · Answer 7 · 2026-04-16 17:43:18

55

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score 74 · Answer 8 · 2026-03-26 14:29:05

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score 121 · Answer 9 · 2026-04-16 06:43:22

121

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List Question

Let $A=\mathbb Q[x_1,...,x_n]$ and let $M$ be an $A$-module. Show that $l_A(M)$ is finite if and only if $\dim_{\mathbb Q}(M)$ is finite.

Left invertible non-square matrices and their sub-matrices over a commutative ring

Quick questions about an exercise in basic module theory

Quick question about the definition of Simple Modules.

Is this functor exact?

Question about a solution to the exercise: Show that $rM=M_s,$ if $\mathrm{gcd}(r,s)=1.$

How is $M^*\otimes M$ identified with $\text{End}(M)$ in the category of $R$-modules?

If $M$ is a flat $A$-module, then is $M$ a flat $A/I$ module?

Dual space of $\mathbb{R}^{\mathbb{N}}$ as an infinite-dimensional vector space over $\mathbb{R}$.

"Distributive property" and "Ring homomorphism" with $A \otimes_R B$

On the correspondent relationship between modules and forms

$P$ is projective implies $P℘$ is a free $R℘$-module

How Should I write this Tensor Product?

Why Are these Elements Not in the Ideal?

Question about the definition of finitely generated module

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