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

Abstract Algebra 16 Finish

Browse Source
This commit is contained in:
Indigo5684
2025-09-30 13:19:29 -05:00
parent 6fe2a46ab6
commit eb9295784d
2 changed files with 25 additions and 2 deletions
Download Patch File Download Diff File Expand all files Collapse all files

3
docs/math/abstract-algebra/DF-12-modules-pids.md
View File

@@ -1,4 +1,4 @@
# Dummit & Foote Chapter 10 Chapter 12 - Modules over Principal Ideal Domains
# Dummit & Foote Chapter 12 - Modules over Principal Ideal Domains
## Section 12.1 The Basic Theory
@@ -50,4 +50,3 @@ Additionally, if $R$ is a PID, as $\Ann_R(N)$ is an ideal, $\Ann(N) = (n)R$ and
1. $N$ is a free submodule with rank $n \leq m$.
2. There exists a basis $y_1, y_2, \ldots, y_m$ of $M$ so that $r_1 y_1, r_2 y_2, \ldots, r_m y_n$ is a basis of $N$ for some $r_i \in R$ and $r_1 | r_2 | \ldots | r_n$