Definition 2.7.3.  Let R be a semiring. We define
(R)
by:
([R, ⊕, 0, ⊙, 1]) := R  (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)
We write “let a ∈ R” for “let a ∈ (R).”
Remarks.

This definition retrieves a representative carrier set from a semiring (which is actually an equivalence class of semirings), and enables typical abuse of notation.