# Differences

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partial_monoids [2018/07/23 17:42] jipsen created |
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====Definition==== | ====Definition==== | ||

- | A \emph{partial monoid} is a structure $\mathbf{A}=\langle A,\cdot,e\rangle$, where $\langle A,\cdot,e\rangle$ is a [[partial semigroup]] and | + | A \emph{partial monoid} is a structure $\mathbf{A}=\langle A,\cdot,e\rangle$, where $\langle A,\cdot\rangle$ is a [[partial semigroup]] and |

$e$ is an identity for $\cdot$: $x\cdot e=x=e\cdot x$ for all $x\in A$. | $e$ is an identity for $\cdot$: $x\cdot e=x=e\cdot x$ for all $x\in A$. |

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