Tying up baric algebras

Antonio M. Oller-Marcén

doi:10.2478/s12175-012-0051-8

paper

Tying up baric algebras

arXiv:1107.5923 · doi:10.2478/s12175-012-0051-8

Abstract

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 $A_{1} \oplus A_{2}$ , 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.

To appear in Mathematica Slovaca