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contents/algebra.tex : Fixed unital magma definition and added unital element is unique proof

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saundersp 2025-02-12 19:02:13 +01:00
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contents/algebra.tex
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@ -13,9 +13,17 @@
\langsubsection{Magma unital}{Unital magma} \langsubsection{Magma unital}{Unital magma}
\begin{definition_sq} \label{definition: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} \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} \subsection{Monoïde}
\begin{definition_sq} \label{definition:monoid} \begin{definition_sq} \label{definition:monoid}