Definition 2.8.6. Let
R be a
ring,
a ∈ R. We define:
−a := ⊖(a) 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)