# Semigroup ## Metadata **Status**:: #x **Zettel**:: #zettel/literature **Created**:: [[2024-03-27]] ## Synopsis Semigroup is a [[Magma]] and the binary operator is associative. - Semigroup is a set U under the binary operator ⨁. - ([[Magma]]) The binary operator is closed: $\forall a, b \in U: a \oplus b \in U$ - (Semigroup) The binary operator is associative: $(a \oplus b) \oplus c = a \oplus (b \oplus c)$