Abstract
Linear algebra tools are used to give a new approach to the open problem of the classification of Bernstein algebras. We prove that any Bernstein algebra [Formula: see text] is isomorphic to a semidirect product [Formula: see text] associated to a commutative algebra [Formula: see text] such that [Formula: see text], for all [Formula: see text] and an idempotent endomorphism [Formula: see text] of [Formula: see text] satisfying two compatibility conditions. The set of types of [Formula: see text]-dimensional Bernstein algebras is parametrized by an explicitly constructed classified object. The automorphisms group of any Bernstein algebra is described as a subgroup of the canonical semidirect product of groups [Formula: see text].
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