Binary Operator (original) (raw)
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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, 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. New York: Holden-Day, 1968.
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Cite this as:
Weisstein, Eric W. "Binary Operator." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BinaryOperator.html