One-dimensional subalgebras of a Bernstein algebra (Q1803021)

A finite-dimensional commutative algebra over a field \(K\) is called a Bernstein algebra if there exists a nontrivial homomorphism \(\omega :A\to K\) (baric algebra) such that the identity \((x^2)^2=\omega(x)^2x^2\) holds in \(A\). If a Bernstein algebra over a field \(K\), char. \(K\) not 2, it is known that a 1-dimensional subalgebra is generated by an idempotent element or by an element of square equal to zero. The aim of this paper is to study the subalgebras generated by two 1-dimensional subalgebras of the given Bernstein algebra \(A\). This can be used to obtain additional information on the lattice isomorphisms between Bernstein algebras.