# 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: $(a \oplus b) \oplus c = a \oplus (b \oplus c)$