Properties of binary operations

property of binary operations, for which changing the order of the operands does not change the result

property of binary operations allowing sequences of operations to be regrouped without changing their value

property involving two mathematical operations

special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them

thumb|On/Off buttons of a train's destination sign control panel. Pressing the On button (green) is an idempotent operation, since it has the same effect whether done once or multiple times. Likewise, pressing Off is idempotent. Idempotence (, ) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of places in abstract algebra (in particular, in the theory of projectors and closure operators) and functional programming (in whi

function that is invariant under all permutations of its variables

mathematical property

Property of some binary operations, such as the cross product and any ring's commutator

set of related mathematical properties

property of a binary operation

In abstract algebra, alternativity is a property of a binary operation. A magma is said to be ' if (xx)y = x(xy) for all x, y \in G and if y(xx) = (yx)x for all x, y \in G. A magma that is both left and right alternative is said to be '.

algebra whose internal binary operation over its base set is associative and commutative at least for any triplet of the same base set whose first and last of the three items are equal