Definition 2.8.8. Let
R be a
ring. We define
[R, +]
by:
[[R, ⊕, 0, ⊖, ⊙, 1], +] := [R, ⊕, 0, ⊖] is a group (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.