Definition
A set of elements combined with one or more operations that act on those elements.
Summary
flowchart BT
sg[Semigroup]
m[Monoid]
cm[Commutative Monoid]
g[Group]
ag[Abelian Group]
mod[Module]
v[Vector Space]
r[Ring]
dr[Division Ring]
cr[Commutative Ring]
f[Field]
m -->|"$a+0=a$"|sg
g -->|"$a-a=0$"|m
cm -->|"$a+b=b+a$"|m
ag -->|"$a-a=0$"|cm
ag -->|"$a+b=b+a$"|g
r -->|"$+$"|ag
r -->|"$\times$"|m
mod -->|"$+$"|ag
mod -->|"$\cdot$"|r
v -->|"$+$"|ag
v -->|"$\cdot$"|f
dr -->|"$a/a=1$"|r
cr -->|"$ab=ba$"|r
f -->|"$ab=ba$"|dr
f -->|"$a/a=1$"|cr