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

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

@@ -2493,7 +2493,7 @@ \end{enumerate}
 
 
   \vspace{1.0cm}
-  This is stated in the Atiyah and MacDonald book (\cite{am}) for mulitple nodes and multilinear maps:
+  This is stated in the Atiyah and MacDonald book (\cite{am}) for multiple nodes and multilinear maps:
 
   \begin{prop}{2.12}
     Let $M_1, \ldots, M_r$ be $A$-modules. Then $\exists ~ (T, g)$ with $T$ an $A$-module, and $g$ a multilinear map $g: M_1 \times \ldots \times M_r \longrightarrow T$, with the following property:
@@ -2503,7 +2503,7 @@
     Moreover, if $(T,g)$ and $(T',g')$ are two pairs with this property, then $\exists !~ j: T \stackrel{iso}{\longrightarrow} T'$ such that $j \circ g = g'$.
   \end{prop}
 
-  \subsection{Usefullness of Tensor Product's Universal Property}
+  \subsection{Usefulness of Tensor Product's Universal Property}
   Anytime we define a function on the T.P. we need to know that it is well defined and linear. This is hard in general because of all the relations of the elements of the T.P..
 
   But using the U.P. of T.P. we can remove all of the extra work and just look at a bilinear map on the cartesian product, which is a much easier object to work with.