M commutative-algebra-notes.pdf → commutative-algebra-notes.pdf

M commutative-algebra-notes.tex → commutative-algebra-notes.tex

@@ -1798,7 +1798,7 @@ (alternatively: the only invertible elements in a polynomial ring over a field are the non-zero constants of the field $k$).
 
   Therefore, $R=k[y_1, \ldots, y_r]$ can be a field iff $r=0$, and we know that is a field, therefore $r=0$ and $R=k$.
 
-  By Noether normalization, at the previus step we knew that $K$ is integral over $R$ ($=k$).
+  By Noether normalization, at the previous step we knew that $K$ is integral over $R$ ($=k$).
 
   \vspace{0.3cm}
   By \ref{integral-implies-finite}, a fingen algebra that is integral over its base field is a finite vector space over that field.