- #1

- 229

- 0

Let I = Q_1 n ... n Q_r = J_1 n ... n J_r be two primary decompositions of I.

How can I show the number of irreducible components in each decomposition is the same?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter ircdan
- Start date

- #1

- 229

- 0

Let I = Q_1 n ... n Q_r = J_1 n ... n J_r be two primary decompositions of I.

How can I show the number of irreducible components in each decomposition is the same?

- #2

matt grime

Science Advisor

Homework Helper

- 9,420

- 4

- #3

- 229

- 0

Matt, thank you very much for your reply. Yes the result is true. I'm assuming all uniqueness theorems found in say, Dummit and Foote. I figured it would be easier to prove with some theory in place, hence why I have r on both sides. Whether I need this or not I don't know, but I figured it might make things easier.

Any help would be greatly appreciated.

Last edited:

- #4

matt grime

Science Advisor

Homework Helper

- 9,420

- 4

- #5

mathwonk

Science Advisor

Homework Helper

- 11,307

- 1,522

i think you need also to assume the decompositions are irredundant, or it is not true.

Share:

- Replies
- 3

- Views
- 2K