Abstract
In this paper we extend a recent result of Liu ([6]) to a larger class of algebras which includes all well-known algebras. The main theorem here states: if the Wedderburn-Malcev theorem (it is called the Levi-Malcev-Harish-Chandra theorem in Lie algebra over a field of characteristic 0) holds for a certain variety of finite-dimensional algebra, then it holds for the same variety of algebras which are local subideal finite. We do not use the trace argument in this paper as which was heavily depended on in ([6]). Hence the result is independent of the characteristics of the ground field F.
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