kruby/notes-archive
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Migrate to KaTeX

Browse Source
This commit is contained in:
Indigo5684
2025-09-30 13:19:34 -05:00
parent e3b95ba3b3
commit 6ed3c08d70
27 changed files with 369 additions and 391 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
docs/math/abstract-algebra/18-integral-domains.md
View File

@@ -53,7 +53,7 @@ Additionally, $F_D$ is unique. That is, given field $E$ such that $E \supset D$,
**Lemma**. 18.14: Let $D$ be a PID. Let $I_1 \subseteq I_2 \subseteq \ldots$. Then, there exists some integer $N$ such that $I_n = I_N$ for all $n > N$. That is, any chain of ideals converges.
**Definition**. Any commutative ring that satisfies the above condition (the *ascending chain condition*), even if it's not a PID, is called a *Noetherien ring*.
**Definition**. Any commutative ring that satisfies the above condition (the *ascending chain condition*), even if it's not a PID, is called a *Noetherian ring*.
**Theorem**. 18.15: Every PID is a UFD. Note that the converse is not true.