port initial notes on commutative algebra (ideals, modules, Noetherian rings) (#1)

* port initial notes on commutative algebra: ideals & modules, Nakayama's lemma, etc

* port notes on Noetherian rings&modules

* add ideals related definitions

* improve Cayley-Hamilton proof (specially determinant trick explanation)

* polishing

* add typos detection

* add some exercises, and proof of Z and K[X} being PID

.github/workflows/typos.toml

@@ -0,0 +1,10 @@
+[default.extend-words]
+thm = "thm"
+
+# equations stuff
+ba = "ba"
+nd = "nd"
+
+# names
+Strang = "Strang"
+Bootle = "Bootle"

.github/workflows/typos.yml

@@ -0,0 +1,21 @@
+name: typos
+on:
+  pull_request:
+    branches: [ main ]
+    types: [ready_for_review, opened, synchronize, reopened]
+  push:
+    branches:
+      - main
+
+jobs:
+  typos:
+    if: github.event.pull_request.draft == false
+    name: Spell Check with Typos
+    runs-on: ubuntu-latest
+    steps:
+    - uses: actions/checkout@v4
+    - name: Use typos with config file
+      uses: crate-ci/typos@master
+      with: 
+        config: .github/workflows/typos.toml
+