A near ring (or semiring) is
a structure with addition and composition. Under addition, the structure is a
commutative group. Composition is associative and distributive on one side:
(p + q) ∘r = p∘r + q ∘r. An example is the set of polynomials with coefficients from
the ring of integers [or indeed from any ring]; composition is ordinary composition of
polynomials. Another example is the set of endomorphisms of an abelian
group.