A binary operator is an operator defined on a set which takes two elements from as inputs and returns a single element of . Binary operators are called compositions by Rosenfeld (1968). Sets possessing a binary multiplication operation include the group, groupoid, monoid, quasigroup, and semigroup. Sets possessing both a binary multiplication and a binary addition operation include the division algebra, field, ring, ringoid, semiring, and unit ring.

See also

AND, Binary Operation, Boolean Algebra, Connective, Division Algebra, Field, Group, Groupoid, Infix Notation, Monoid, NOT, Operator, OR, Quasigroup, Ring, Ringoid, Semigroup, Semiring, Set Closure, Unit Ring, XNOR, XOR

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References

Rosenfeld, A. An Introduction to Algebraic Structures. San Francisco, CA: Holden-Day, 1968.

Referenced on Wolfram|Alpha

Binary Operator

Cite this as:

Weisstein, Eric W. "Binary Operator." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BinaryOperator.html

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