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 ?
With this in mind, in this section we give a description of Nakayama automorphism for these non-commutative algebras using the Nakayama automorphism of the ring of the coefficients.
The difference which makes this extension non-obvious is that a time-invariant system is described by two non-commutative polynomials while a time-varying system requires three polynomials, and the third one has to be incorporated into the analysis.
We concentrate on non-commutative cryptography and find that we can use the non-Abelian Group to design the new scheme.
Horvathy, "Chiral decomposition in the non-commutative Landau problem," Annals of Physics, vol.
Pseudo-product algebras, the non-commutative generalizations of Haajek's product algebras [18], were introduced in 2002 [6].
Gouba, "Classical limits of quantum mechanics on a non-commutative configuration space," Journal of Mathematical Physics, vol.
Part four introduces the concept of non-commutative geometry and uses it to analyze microscopic theory.
So the attitudinizing title refers to the vector space dimensions: we obtain a 3 dimensional non-commutative algebra as a weak wreath product of two 2 dimensional commutative algebras.
Let R be a non-commutative prime ring, a, b [member of] R, I [a.sub.n] two-sided ideal of R, n [greater than or equal to] 1 a fixed integer such that [a[[r.sub.1], [r.sub.2]] + [[r.sub.1], [r.sub.2]]b, [[[r.sub.1], [r.sub.2]].sup.n]] [member of] Z(R), for any [r.sub.1], [r.sub.2] [member of] I.
An -semigroup is a non-associative and non-commutative algebraic structure mid way between a groupoid and a commutative semigroup.
In 1993 new ideas appeared in asymmetric cryptography [6]--using known hard computational problems in infinite non-commutative groups instead of hard number theory problems such as discrete logarithm or integer factorization problems.
The findings of this study showed the difficulty young children have in perceiving and understanding the non-commutative nature of 3D rotation and the power of the computational VRLE in giving students experiences that they rarely have in real life with 3D manipulations and 3D mental movements.

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