The Bar-Radical of a Class of Almost Alternative Baric Algebras

Abstract

In this article we prove that, if (U, ω) is a finite dimensional baric algebra of (γ, δ) type over a field F of characteristic ≠ 2,3,5 such that γ2 − δ2 + δ = 1 and δ ≠ 0,1, then rad(U) = R(U) ∩ (bar(U))2, where R(U) is the nilradical (maximal nil ideal) of U.