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, XOR## Explore with Wolfram|Alpha

## References

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. https://mathworld.wolfram.com/BinaryOperator.html