migrate dremark

2021_Algebra_I.tex

@@ -1844,9 +1844,9 @@ Let $R = \mathfrak{k}[X_1,\ldots,X_n]$ and $I \subseteq R$ an ideal.
 \begin{corollary}\label{codimintersection}
     Let $A$ and $B$ be irreducible subsets of $\mathfrak{k}^n$. If $C$ is an irreducible component of $A \cap B$, then $\codim(C, \mathfrak{k}^n) \le  \codim(A, \mathfrak{k}^n) + \codim(B, \mathfrak{k}^n)$.
 \end{corollary}
-\begin{dremark}
+\begin{remark}+
     Equivalently, $\dim(C) \ge \dim(A) + \dim(B)-n$. 
-\end{dremark}
+\end{remark}
 \begin{proof}
     Let $X = A \times  B \subseteq \mathfrak{k}^{2n}$, where we use $(X_1,\ldots,X_n,Y_1,\ldots,Y_n)$ as coordinates of $\mathfrak{k}^{2n}$.
     Let $\Delta \coloneqq \{(x_1,\ldots,x_n,x_1,\ldots,x_n) | x \in \mathfrak{k}^n\} $ be the diagonal in $\mathfrak{k}^n \times  \mathfrak{k}^n$.