In this paper n-ary regular division associative algebras are discussed. It is shown that every operation in algebra will be endo-linearly represented over the same binary group. Schauffler like theorem proved for those algebras.

where multiplication is denoted by juxtaposition; note the absence of associativity. A division algebra is a nontrivial algebra in which division is possible: for any a ∈ V and any nonzero b ∈ V , there exists precisely one element x with a = bx and precisely one element y with a = yb. A normed division algebra is a division algebra with a norm ||·|| satisfying ||xy|| = ||x|| ||y||. There are p...

In his recent series of lectures, Prof. B. I. Plotkin discussed geometrical properties of the variety of associative K-algebras. In particular, he studied geometrically noetherian and logically noetherian algebras and, in this connection, he asked whether there exist uncountably many simple K-algebras with a fixed finite number of generators. We answer this question in the affirmative using bot...

In this paper we study division algebras over the function fields of curves over Qp. The first and main tool is to view these fields as function fields over nonsingular S which are projective of relative dimension 1 over the p adic ring Zp. A previous paper showed such division algebras had index bounded by n assuming the exponent was n and n was prime to p. In this paper we consider algebras o...

Abstract We propose a new identification system based on algorithmic problems related to computing isomorphisms between central simple algebras. design statistical zero knowledge protocol which relies the hardness of orders in division algebras generalizes by Hartung and Schnorr, integral equivalence quadratic forms.

In this paper we find a field such that the algebras obtained by the Cayley-Dickson process are division algebras of dimension 2t,∀t ∈ N. Subject Classification: 17D05; 17D99. From Frobenius Theorem and from the remark given by Bott and Milnor in 1958, we know that for n ∈ {1, 2, 4} we find the real division algebras over the real field R. These are: R, C, H(the real quaternion algebra), O(the ...

The category of all 2-dimensional real division algebras is shown to split into four full subcategories each of which is given by the natural action of a Coxeter group of type A1 or A2 on the set of all pairs of ellipses in R which are centred in the origin and have reciprocal axis lengths. Cross-sections for the orbit sets of these group actions are being determined. They yield a classificatio...