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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, Boolean Algebra, Closure, Division Algebra, Field, Group, Groupoid, Monoid, Operator, Or, Monoid, Not, Quasigroup, Ring, Ringoid, Semigroup, Semiring, XOR, Unit Ring


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

© 1996-9 Eric W. Weisstein