Definition 2.7.8.  Let R be a semiring. We define
1R
by:
1[R,⊕,0,⊙,1] := 1  (R is a set, ⊕ : R × R → R is an operation on R, 0 ∈ R, ⊙ : R × R → R is an operation on R, 1 ∈ R such that (R, ⊕, 0, ⊙, 1) forms a semiring)