From e78d54c45f19eaf05cf3e691fffdfd5ae94ffa55 Mon Sep 17 00:00:00 2001
From: saundersp <pierre.saundersgb@gmail.com>
Date: Wed, 12 Feb 2025 19:02:13 +0100
Subject: [PATCH] contents/algebra.tex : Fixed unital magma definition and
 added unital element is unique proof

---
 contents/algebra.tex | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/contents/algebra.tex b/contents/algebra.tex
index 97e0fb9..6aae4b0 100644
--- a/contents/algebra.tex
+++ b/contents/algebra.tex
@@ -13,9 +13,17 @@
 \langsubsection{Magma unital}{Unital magma}
 
 \begin{definition_sq} \label{definition:unital_magma}
-	Un magma \ref{definition:magma} $(E, \star)$ est dit \textbf{unital} si $\exists 0_E \in E, \forall a \in E, 0_E \star a = a$.
+	Un magma \ref{definition:magma} $(E, \star)$ est dit \textbf{unital} si $\exists 0_E \in E, \forall a \in E, 0_E \star a =  a \star 0_E = a$.
 \end{definition_sq}
 
+\begin{theorem_sq}
+	L'élément neutre d'un magma unital $(E, \star)$ est unique.
+\end{theorem_sq}
+
+\begin{proof}
+	Soit $e, f$ deux éléments neutres d'un magma unital $(E, \star)$, par définition d'un élément neutre, on peut poser $e = e \star f = f = f \star e = e$
+\end{proof}
+
 \subsection{Monoïde}
 
 \begin{definition_sq} \label{definition:monoid}