Commutativity


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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].

References in periodicals archive ?
Koc, Notes on commutativity of prime rings with generalized derivations, Commun.
In addition, teachers can show that 3 rows of 4 is grouped differently to 4 rows of 3, yet the total is the same--the idea of commutativity.
The R-weakly commutativity of type (P) of f and g yields G(f f[x.
In the present paper we concern with the multiplication and commutativity properties of the Berezin transform in the case of pluriharmonic functions defined on the unit ball B in [C.
The general theorem introduced and proved here clearly eliminates the need to prove any fixed point theorems for specific expansive maps satisfying any of the generalized commutativity conditions such as weakly commuting, compatibility of type ( A), etc.
Commutativity and being a band or a semilattice are invariant properties of Morita equivalent posemigroups with common (two-sided weak) local units.
The gyrations, which possess their own rich structure, measure the extent to which Einstein addition deviates from commutativity and associativity as we see from the following identities [1, 11, 12]:
If we follow the real or complex case for defining derivatives, we have two possibilities because of the non commutativity of the multiplication in H, namely
23)], we can easily verify the commutativity of the fractional integral operators involved in the composition formulas (2.
1] due to Commutativity of + (recall that the structure <R, +,.
For example, if alternate representational systems offer clearer, richer explanations of concepts such as equality or commutativity, or simply if more time is taken to discuss a strategy, understanding and proficiency in math may increase.
The example also shows that the requirement of commutativity in Theorem 2.