Definition 2.8.18. Let
R be a
ring. We define:
[R×] := [R×, ⊙∣R×, 1, (R× → R×a ↦ a-1)] if R = [R, ⊕, 0, ⊖, ⊙, 1] (R is a set, ⊕ : R × R → R is an operation on R, 0 ∈ R, ⊖ : R → R is a function, ⊙ : R × R → R is an operation on R, 1 ∈ R such that (R, ⊕, 0, ⊖, ⊙, 1) forms a ring) References.