Bernstein algebras were introduced by Holgate [6] as an algebraic formulation of the problem of classifying the stationary evolution operators in genetics (see [8]). Since then, many authors have contributed to the study of these algebras, and there is a fairly extensive bibliography on the subject. Known results include classification theorems for sorre types of Bernstein algebras (for instanc...

We introduce the notions of strongly zero-product (strongly Jordan zero-product) preserving maps on normed algebras. These notions are generalization of the concepts of zero-product and Jordan zero-product preserving maps. Also for a non-zero vector space V and for a non-zero linear functional f on V, we equip V with a multiplication, converting V into an associative algebra, denoted by Vf . We...

Let A be a prime *-algebra. In this paper, we suppose that ? : satisfies ?(A B) = ?(A) B + ?(B) where A*B B*A for all A, A. Then, is an additive *-derivation.

The product of two Heisenberg-Weil algebras contains the Jordan-Schwinger representation of su(2). This Algebra is quotiented by the square-root of the Casimir to produce a non-associative algebra denoted by Ψ. This algebra may be viewed as the right-module over one of its associative subalgebras which corresponds to the algebra of scalar fields on the noncommutative sphere. It is now possible ...

In this letter I discuss how conformal geometric algebra models for Euclidean and Minkowksi spaces determine allowed quantum mechanical statespaces for free particles I explicitly treat (1 + 1)-dimensional spacetime and 2-dimensional Euclidean space.