Acerca de álgebras báricas satisfaciendo \((x^2)^2 = w(x)^3x *\)

Abstract

Let (A, ðœ”) be a baric algebra, we define the E-ideal associated to the train polynomial p(ð“) = ð“ⁿ + y₁ðœ”(ð“)ð“^n-1 + ... + y_n-1ðœ”(ð“)^n-1ð“, by the ideal E_A(p) de A generated by all p(a), a ⋲ A. Different train polynomials may give rise to the same E-ideal. Two train polynomials p(ð“) and q(ð“) are equivalent when E_A(p) = E_A(q). We prove tbat for baric algebras satisfying (ð“²)² = ðœ”(ð“)³ð“ there are 3 equivalence classes of train polynomials.