On Bernstein and train algebras of rank 31

摘要

In this paper we prove that if (A, #x3C9;) is a Bernstein algebra or a train algebra of rank 3, then the bar-radical of (A,#x3C9;) is (bar(A))2and that it is nilpotent (hence solvable). We give also a description of a class of train algebras of rank 3, defined by pairs of bilinear mappings.