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$E$-ideals in Bernstein algebras. (English) Zbl 0968.17013
Costa, Roberto (ed.) et al., Nonassociative algebra and its applications. Proceedings of the fourth international conference, São Paulo, Brazil. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 211, 35-42 (2000).
Let $A$ be a commutative (not necessarily associative) algebra over a field $F$ ($\text{char}(F)\not= 2$), and $\omega : A \rightarrow F$ a nonzero homomorphism. The ordered pair $(A, \omega$) is called a baric algebra and $\omega$ its weight. $(A, \omega$) is called a Bernstein algebra if $(x^2)^2 = \omega(x)^2 \cdot x^2$, for all $x \in A$. In this paper E-ideals in baric algebras and E-ideals in Bernstein algebras are studied. Some examples are constructed that there exist infinite dimensional Bernstein algebras with few E-ideals and also algebras with an infinite number of E-ideals. For the entire collection see [Zbl 0940.00027].
17D92Genetic algebras