The Wedderburn b-decomposition for a class of almost alternative baric algebras

In this paper we deal with the Wedderburn b-decomposition for baric algebras of (γ, δ) type.

ON SOME JORDAN BARIC ALGEBRAS

Several classes of baric algebras studied by different authors will be given a unified treatment, using the technique of gametization. Most of these algebras will be shown, using straightforward arguments, to be either Jordan algebras or closely related to them.

Tying up baric algebras

Given two baric algebras (A 1, ω 1) and (A 2, ω 2) we describe a way to define a new baric algebra structure over the vector space A 1 ⊕ A 2, which we shall denote (A 1 ⋈ A 2, ω 1 ⋈ ω 2). We present some easy properties of this construction and we show that in the commutative and unital case it preserves indecomposability. Algebras of the form A 1 ⋈ A 2 in the associative, coutable-dimensional, zero-characteristic case are classified.

E-Ideals in baric algebras: basic properties

In this work we introduce the notion of E-ideal, generalizing I. M. H. Etherington's idea. We study the general characteristics of the lattice of E-ideals in baric algebras, and some properties inherited from an arithmetic of train polynomials.