Definition:Additive Semiring

Definition
An additive semiring is a semiring with a commutative distributand.

That is, an additive semiring is a ringoid $\struct {S, *, \circ}$ in which:
 * $(1): \quad \struct {S, *}$ forms a commutative semigroup
 * $(2): \quad \struct {S, \circ}$ forms a semigroup.

Note on Terminology
Most of the literature simply calls this a semiring; however, on the term semiring is reserved for more general structures, not imposing that the distributand be commutative.

Also see

 * Definition:Ringoid (Abstract Algebra)
 * Definition:Semiring (Abstract Algebra)
 * Definition:Rig
 * Definition:Ring (Abstract Algebra)