diff --git a/algebra.sty b/algebra.sty
index 2b3f4c7..6d24916 100644
--- a/algebra.sty
+++ b/algebra.sty
@@ -37,7 +37,6 @@
 \newcommand{\Vp}{\ensuremath V_{\mathbb{P}}}%\Spec}}
 \newcommand{\Pn}{\bP^n}%\Spec}}
 
-\DeclareMathOperator{\Ker}{Ker}
 \DeclareMathOperator{\nil}{\mathfrak{nil}}
 
 \usetikzlibrary{arrows.meta,
diff --git a/inputs/nullstellensatz_and_zariski_topology.tex b/inputs/nullstellensatz_and_zariski_topology.tex
index 6d94183..e243c80 100644
--- a/inputs/nullstellensatz_and_zariski_topology.tex
+++ b/inputs/nullstellensatz_and_zariski_topology.tex
@@ -680,7 +680,7 @@ Let $R = \mathfrak{k}[X_1,\ldots,X_n]$.
 
 \end{proof}
 \begin{remark}
-    $i$ is often not injective and $\Ker(i) = \{r \in R | \exists s \in S ~ s \cdot r = 0\} $.
+    $i$ is often not injective and $\ker(i) = \{r \in R | \exists s \in S ~ s \cdot r = 0\} $.
     In particular $(r = 1)$, $R_S$ is the null ring iff $0 \in S$.
 \end{remark}
 \begin{notation}