相关论文: Constructing zero divisors in the higher dimension…
In this paper we describe algebraically the zero divirsors of the Cayley- Dickson algebras $\a_{n}=\erre^{2^n}$ for $n \ge 4$ over the real numbers.
Cayley-Dickson algebras are an infinite sequence of non-associative algebras starting with the reals, complexes, quaternions, and octonions. We study the zero-divisors in the higher Cayley-Dickson algebras. In particular, we show that the…
We establish many previously unknown properties of zero-divisors in Cayley-Dickson algebras. The basic approach is to use a certain splitting that simplifies computations surprisingly.
Viewing the Cayley-Dickson process as a graded construction provides a rigorous definition of associativity consisting of three classes and the non-associative parts dividing into four types. These simplify the Moufang loop identities and…
The sedenion algebra $\mathbb S$ is a non-commutative, non-associative, $16$-dimensional real algebra with zero divisors. It is obtained from the octonions through the Cayley-Dickson construction. The zero divisors of $\mathbb S$ can be…
Zero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from N-dimensional hypercomplex numbers (N a power of 2, at least 4) can represent singularities and, as N approaches infinite, fractals -- and thereby,scale-free networks. Any…
In this paper we study the algebra monomorphisms from A_m =R^(2^m) into A_n=R^(2^n) for 0<m<n where the A_k 's are the Cayley- Dickson algebras over the real numbers. We show that for m>2 there are many different types of monomorphisms and…
We develop the basic properties of $R^{(2)}$-modules, introduce the concept of zero divisor manifolds, construct projective $R^{(2)}$-space which generalizes the real projective space, and initiate the study of the counterpart of symplectic…
The article is devoted to the investigation of transformation groups of polynomials over Cayley-Dickson algebras and their manifolds of zeros. The problems about expressibility of zeros with the help of roots and decomposibility of…
A famous conjecture about group algebras of torsion-free groups states that there is no zero divisor in such group algebras. A recent approach to settle the conjecture is to show the non-existence of zero divisors with respect to the length…
In this paper we concern with positive zero divisors in $C^{*}$ algebras. By means of zero divisors, we introduce a hereditary invariant for $C^{*}$ algebras. Using this invariant, we give an example of a $C^{*}$ algebra $A$ and a $C^{*}$…
{\small \ We generalize the concepts of \thinspace level \thinspace and \thinspace sublevel of a composition algebra to division algebras obtained by the Cayley-Dickson process. In 1967, R. B. Brown constructed, for every}$t\in…
In this paper, we generalize the concepts of level and sublevels of a composition algebra to algebras obtained by the Cayley-Dickson process. In 1967, R. B. Brown constructed, for every $t\in \Bbb{N},$ a division algebra $A_{t}$ of…
New families of eight-dimensional real division algebras with large derivation algebra are presented: We generalize the classical Cayley-Dickson doubling process starting with a unital algebra with involution over a field F by allowing the…
The Cayley-Dickson Construction is a generalization of the familiar construction of the complex numbers from pairs of real numbers. The complex numbers can be viewed as two-dimensional vectors equipped with a multiplication. The…
Zero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from N-dimensional hypercomplex numbers (N a power of 2, at least 4) can represent singularities and, as N approaches infinite, fractals -- and thereby,scale-free networks. Any…
We study divisors in a complex manifold in view of the property that the algebra of logarithmic differential operators along the divisor is generated by logarithmic vector fields. We give a sufficient criterion for the property, a simple…
We associate a graph to a possible non-zero zero-divisor in the group algebra of a torsion-free group.
In this paper, we study the zero set of the Hopf construction map F_n : A_n_ x A_n --> A_n x A_0 given by F_n (x, y) = (2xy, | y|^2 - |x|^2) for n >3 where A_n is the Cayley-Dickson algebra of dimension 2^n over the real numbers.
In this paper, \thinspace \thinspace we generalize the concepts of \thinspace level \thinspace and \thinspace sublevel of a composition algebra to algebras obtained by the Cayley-Dickson process. In 1967, R. B. Brown constructed, for…