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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 (char(F)2), and ω:AF a nonzero homomorphism. The ordered pair (A,ω) is called a baric algebra and ω its weight. (A,ω) is called a Bernstein algebra if (x 2 ) 2 =ω(x) 2 ·x 2 , for all xA. 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.
MSC:
17D92Genetic algebras