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.