A semiring is a set together with two Binary Operators satisfying the following conditions:
A semiring is therefore a commutative Semigroup under addition and a Semigroup under multiplication.
A semiring can be empty.
- 1. Additive associativity: For all ,
- 2. Additive commutativity: For all , ,
- 3. Multiplicative associativity: For all ,
- 4. Left and right distributivity: For all ,
See also Binary Operator, Ring, Ringoid, Semigroup
Rosenfeld, A. An Introduction to Algebraic Structures. New York: Holden-Day, 1968.
© 1996-9 Eric W. Weisstein