# Distributivity

*distributivity law, distributive property, of one operation with respect to another*

The property of a pair of binary algebraic operations (cf. Algebraic operation), expressed by one of the following identities:

where are the symbols of the binary operations, and are object variables. If in a set two specific binary operations , are defined, i.e. two mappings

are given, and the symbols are interpreted as the symbols of the respective operations in , one can speak of the truth or falsehood of each one of the formulas D1 and D2 in . If both these formulas are true in , the operation is called distributive with respect to the operation in .

#### Comments

I.e., in the operation is distributive with respect to if for all one has and .

For example, multiplication is distributive with respect to addition in the set of real numbers and in the set of integers.

**How to Cite This Entry:**

Distributivity.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Distributivity&oldid=14448