get rid of legacy macros

algebra.sty

@@ -37,14 +37,9 @@
 \newcommand{\Vp}{\ensuremath V_{\mathbb{P}}}%\Spec}}
 \newcommand{\Pn}{\bP^n}%\Spec}}
 
-\newcommand{\npr}{\footnote{Not relevant for the exam.}}
-\newcommand{\limrel}{\footnote{Limited relevance for the exam.}} % may appear in 3x questions
-%\DeclareMathOperator{\ev}{ev}
 \DeclareMathOperator{\Ker}{Ker}
 \DeclareMathOperator{\nil}{\mathfrak{nil}}
-%\DeclareMathOperator{\rad}{\mathfrak{rad}}
+
-\RequirePackage{stackengine}
-\stackMath
 \usetikzlibrary{arrows.meta,
 	quotes, babel}
 
@@ -53,3 +48,6 @@
 \def\existsone{\exists!}
 \def\defon#1{\upharpoonright_{#1}}
 \DeclareMathOperator{\Id}{Id}
+
+% \RequirePackage{stackengine}
+% \stackMath

inputs/nullstellensatz_and_zariski_topology.tex

@@ -1549,7 +1549,7 @@ Let $R = \mathfrak{k}[X_1,\ldots,X_n]$ and $I \subseteq R$ an ideal.
 \end{remark}
 
 \subsubsection{Application to the property of being a UFD}
-\begin{proposition}\limrel
+\begin{proposition}
     Let $R$ be a Noetherian domain. Then $R$ is a UFD iff every $\fp \in \Spec R$ with $\hght(\fp)= 1$\footnote{In other words, every  $\subseteq$-minimal element of the set of non-zero prime ideals of $R$ } is a principal ideal.
 \end{proposition}
 \begin{proof}
@@ -1565,7 +1565,7 @@ Let $R = \mathfrak{k}[X_1,\ldots,X_n]$ and $I \subseteq R$ an ideal.
     Thus $\fp = pR$ for some prime element $p$. We have $p | f$ since $f \in \fp$. As $f$ is irreducible, $p$ and $f$ are multiplicatively equivalent. Thus $f$ is a prime element.
 \end{proof}
 
-\subsection{The Jacobson radical}\limrel
+\subsection{The Jacobson radical}
 \begin{proposition}
     For a ring $A, \bigcap_{\mathfrak{m} \in \MaxSpec A} \mathfrak{m} = \{a \in A | \forall x \in  A ~ 1 - ax \in A^{\times }\} \text{\reflectbox{$\coloneqq$}} \rad(A)$, the \vocab{Jacobson radical}  of $A$.
 \end{proposition}