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 ?
Non-commutative algebraic geometry, Springer-Verlag, Berlin, 1981.
In the discrete-time case the definition of the transfer function is based on a non-commutative twisted polynomial ring, which is a special case of the skew polynomial ring and can be embedded into its quotient field by the Ore condition.
n] [member of] Z(R), for any x [member of] L, a non-commutative Lie ideal of R and n [greater than or equal to] 1 a fixed integer.
Calculus, manifolds, tensors, non-commutative geometries, etc.
8, we give a new interpretation to the Leray number of the clique complex of a graph in terms of non-commutative algebra.
Non-commutative geometry is an increasingly-studied field by researchers and graduate students in mathematics and mathematical physics to shed new light on the traditional commutative case.
The study of these objects and their representation theory has opened up important new directions in non-commutative algebra.
Topics of the papers include finite field experiments, K3 surfaces of Picard Rank One (which are double covers of the projective plane), Beilinson conjectures in the non-commutative setting, rational curves on cubic hypersurfaces, Abelian varieties over finite fields, global information from computations over finite fields, the geometry of Shimura varieties of the Hodge type over finite fields, Zeta functions over finite fields, de Rham cohomology of varieties over fields of positive characteristics, and homomorphisms of Abelian varieties over finite fields.
This paper deals with the constructions of commutative hyperstructures from non-commutative ones.
partial derivative] / [partial derivative]t are non-commutative as [sup.
Moreover we may assume H non-commutative, otherwise also R must be commutative.
This loop is non-commutative and non-associative and of order 6.

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