Binary Operator

An operator defined on a set S which takes two elements from S as inputs and returns a single element of S. 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, Monoid, NOT, Operator, OR, Quasigroup, Ring, Ringoid, Semigroup, Semiring, Set Closure, Unit Ring, XNOR, XOR

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

Referenced on Wolfram|Alpha

Binary Operator

Cite this as:

Weisstein, Eric W. "Binary Operator." From MathWorld--A Wolfram Web Resource.

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