Lemma 10.52.14 (02M2)—The Stacks project

Processing math: 100%

Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.52: Length
Lemma 10.52.14 (cite)

previous lemma

numberstags

history
statistics
2 tags refer to this tag

Lemma 10.52.14. Let $A \to B \to C$ be flat local homomorphisms of local rings. Then

$\text{length}_ B(B/\mathfrak m_ A B) \text{length}_ C(C/\mathfrak m_ B C) = \text{length}_ C(C/\mathfrak m_ A C)$

Proof. Follows from Lemma 10.52.13 applied to the ring map $B \to C$ and the $B$ -module $M = B/\mathfrak m_ A B$ $\square$

Comments (0)

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 (0)

Post a comment