Primitive algebras with involution
Wallace S. Martindale · Pacific Journal of Mathematics · 1961
element satisfies a non-trivial polynomial equation f(t) = 0, where f(t) = Σ<****» a i e Φ One can show that every algebraic algebra is an I-algebra.In the proof of this fact (see [1], p. 210, Proposition 1), however, the following sharper result is obtained.REMARK 4. Let a be a non-nilpotent element of an algebraic algebra.Then the subalgebra [[a]] generated by a contains a nonzero idempotent.An involution* of an algebra A over Φ is an anti-automorphisrn of A of period 2, that is, A similar proof was communicated orally to the author by I. N. Herstein.