Lemma 10.52.2 (02LZ)—The Stacks project

Loading [MathJax]/extensions/tex2jax.js

Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.52: Length
Lemma 10.52.2 (cite)

previous definition
next lemma

numberstags

history
statistics
1 tag refers to this tag

Modules of finite length are finite.

Lemma 10.52.2. Let $R$ be a ring. Let $M$ be an $R$-module. If $\text{length}_ R(M) < \infty $ then $M$ is a finite $R$-module.

Proof. Omitted. $\square$

Comments (1)

Comment #1368 by Herman Rohrbach on March 20, 2015 at 13:27

Suggested slogan: Modules of finite length are finite.

There are also:

2 comment(s) on Section 10.52: Length

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (1)

Post a comment