Example 15.8.5 (07ZB)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 15: More on Algebra
Section 15.8: Fitting ideals
Example 15.8.5 (cite)

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Example 15.8.5. Let $R$ be a ring. The Fitting ideals of the finite free module $M = R^{\oplus n}$ are $\text{Fit}_ k(M) = 0$ for $k < n$ and $\text{Fit}_ k(M) = R$ for $k \geq n$ .

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Comment #8245 by Laurent Moret-Bailly on March 06, 2023 at 10:08

Other interesting examples: if $I, J\subset R$ are ideals, then $\mathrm{Fit}_0(R/I)=I$ , $\mathrm{Fit}_0(R/I\oplus R/J)=IJ$ , $\mathrm{Fit}_1(R/I\oplus R/J)=I+J$ . The first could also be in 15.8.4.

Comment #8891 by Stacks project on April 09, 2024 at 11:29

Thanks very much! I put these in their own example environment. Changes are here.

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