Commutativity


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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Commutativity

 

a property of the addition and multiplication of numbers expressed by the identities a + b = b + a and ab = ba. In a more general sense, the operation a * b is termed commutative if a * b = b *a. Addition and multiplication of polynomials, for example, have the property of commutativity; vector multiplication (see VECTOR PRODUCT) is not commutative since [a,b] = — [b,a].

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
The canonical form is determined up to associativity and commutativity of ??
The case of [M.sub.12] is similar: it has the same 1-simplices as [M.sub.1], and once we impose commutativity of (3.5) on the 3-simplices, any 2-simplex ([phi]|[psi]) must obey (3.4) in order to have a 3-simplex with the boundary of [s.aub.1] ([phi]|[psi]).
Similarly, the unbalanced linguistic generalized weighted geometric Heronian mean operator does not satisfy the property of commutativity. Some special cases of the unbalanced linguistic generalized weighted geometric Heronian mean operator in regard to parameters p and q can be seen in the Appendix.
Recently, [14] studied the algebraic properties of small Hankel operators on the harmonic Bergman space and got very different commutativity of small Hankel operators compared with the case of Toeplitz operators.
Turning to a discussion of commutativity, we now suppose that Z = X so that we can form the compositions b/q [??] a/p, which is an endomorphism of X, and a/p [??] b/q, an endomorphism of Y.
In particular, commutativity conditions for relaxed secondorder systems first appeared in 1982 [13].
We have also studied some desired properties of the developed operators, such as commutativity, idempotency, boundary, etc.
(2010a) developed the induced fuzzy number intuitionistic fuzzy ordered weighted geometric (I-FIFOWG) operator and studied some desirable properties of the I-FIFOWG operators, such as commutativity, idempotency and monotonicity.
The commutativity of the strong product follows from the symmetry of the definition of adjacency and for associativity see [10].
The aleatory contracts represent a distinct species of contracts found in our civil law, being characterized by the alea element (dice, luck, risk, danger, hazard), representing the exceptions to the commutativity, which represents the rule in contractual matters following to which, at the conclusion of a contract, the existence and the extent of the benefits payable by the parties are clear and can be appreciated even at the time.
Commutativity of (S1) is clear from (9) itself; that is, s(A,B) = s(B,A).