distributive law


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distributive law.

In mathematics, given any two operations, symbolized by * and +, the first operation, *, is distributive over the second, +, if a*(b+c)=(a*b)+(a*c) for all possible choices of a, b, and c. Multiplication, ×, is distributive over addition, +, since for any numbers a, b, and c, a×(b+c)=(a×b)+(a×c). For example, for the numbers 2, 3, and 4, 2×(3+4)=14 and (2×3)+(2×4)=14, meaning that 2×(3+4)=(2×3)+(2×4). Strictly speaking, this law expresses only left distributivity, i.e., a is distributed from the left side of (b+c); the corresponding definition for right distributivity is (a+bc=(a×c)+(b×c).

distributive law

[di′strib·yəd·iv ′lȯ]
(mathematics)
A rule which stipulates how two binary operations on a set shall behave with respect to one another; in particular, if +, ° are two such operations then ° distributes over + means a ° (b + c) = (a ° b) + (a ° c) for all a,b,c in the set.
References in periodicals archive ?
In this section we present distributive laws on the collection of neutrosophic soft set.
In the papers [8] and [17], the notion of distributive law was generalized by weakening the compatibility conditions with the units of the monads.
We start Section 1 by recalling from [17] the notion of weak distributive law and the corresponding construction of weak wreath product.
Assuming that there is a strict distributive law eA [cross product] B [right arrow] B [cross product] eA, we extend it to a weak distributive law A [cross product] B [right arrow] B [cross product] A.
k-algebra) R which admits a separable Frobenius structure, we show that any distributive law over R induces a weak distributive law over k.
i] and construct a weak distributive law ([[direct sum].
1], a 2-cell [PSI]: A [cross product] B [right arrow] B [cross product] A is said to be a weak distributive law of A over B if the following diagrams commute.
Students applied the distributive law correctly but made '+' or '-' sign error in the second algebraic term.
For instance, students misapplied the distributive law by multiplying only one of the algebraic terms in the bracket.
These students either conjoined the algebraic terms in bracket or misapplied the distributive law in bracket expansion.
The distributive law is often applied as a strategy to figure out an unknown multiplication fact using known facts.
by resequencing multiplications with several factors or implementing the distributive law of multiplication as compared to addition),