Definition 2.7.9. Let
R be a
semiring. We define
[R, ⋅]
by:
[[R, ⊕, 0, ⊙, 1], ⋅] := [R, ⊙, 1] is a monoid (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) References.