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Field
A
ring
⟨S, ∗1, ∗2⟩ in which ⟨S \ {e1}, ∗2⟩ is a
group
⟨S \ {e1}, ∗2⟩
A group is that every nonidentity element (with respect to ∗1) must have an inverse element (with respect to ∗2)
Finite Group
Group
⟨S, ∗⟩ is finite if
contains only finitely many elements
1