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

$F$ (

$\text{char}\left(F\right)\ne 2$), and

$\omega :A\to F$ 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

${\left({x}^{2}\right)}^{2}=\omega {\left(x\right)}^{2}\xb7{x}^{2}$, 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.