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单词 Semiring
释义

Semiring

A semiring is a set together with two Binary Operators satisfying the following conditions:

1. Additive associativity: For all , ,

2. Additive commutativity: For all , ,

3. Multiplicative associativity: For all , ,

4. Left and right distributivity: For all , and .
A semiring is therefore a commutative Semigroup under addition and a Semigroup under multiplication.A semiring can be empty.

See also Binary Operator, Ring, Ringoid, Semigroup


References

Rosenfeld, A. An Introduction to Algebraic Structures. New York: Holden-Day, 1968.


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