sentences:  A near-semiring is a set "S" with two binary operations "+" and "·", and a constant 0 such that ("S", +, 0) is a monoid (not necessarily commutative), ("S", ·) is a semigroup, these structures are related by a single (right or left) distributive law, and accordingly 0 is a one-sided (right or left, respectively) absorbing element.Formally, an algebraic structure ("S", +, ·, 0) is said to be a near-semiring if it satisfies the following axioms