(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.