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.
Binary Operator
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, XORExplore with Wolfram|Alpha
References
Rosenfeld, A. An Introduction to Algebraic Structures. New York: Holden-Day, 1968.Referenced on Wolfram|Alpha
Binary OperatorCite this as:
Weisstein, Eric W. "Binary Operator." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BinaryOperator.html