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be a commutative (not necessarily associative) algebra over a field
a nonzero homomorphism. The ordered pair
) is called a baric algebra and
) is called a Bernstein algebra if
, for all
. 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.