Abstract
Let ( A, ω) be a finite dimensional Bernstein algebra and N the kernel of ω. We study the algebras where dim N 2 is 1. The algebras fall into two general classes. For the first of these classes we give the multiplication tables for the complete set of nonisomorphic algebras. For the second of these classes we give the multiplication tables for what we call “complete algebras.” We show that any algebra of the second class can be embedded in a complete algebra. The multiplication in the complete algebras is easy to describe. The Bernstein algebras of the second class are then characterized as subalgebras of the complete algebras. For Jordan Bernstein algebras satisfying dim N 2 = 1 we give the complete classification.
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