complete Noetherian rings/modules notes, add Hilbert basis theorem, some Noetherian exercises (#2)

* add proof for split exact sequences

* port exercise R.2.9

* Noetherian rings: add ex. 3.2 & 3.5

* Hilbert basis theorem, Noetherian module properties

* add Noetherian exercises 3.3 & 3.4

.github/workflows/typos.toml

@@ -1,4 +1,9 @@
 [default.extend-words]
+iddeal = "ideal"
+iddeals = "ideals"
+allpha = "alpha"
+
+# strings that are not a typo:
 thm = "thm"
 
 # equations stuff