An algebra A is homogeneous if the automorphism group of A acts transitively on the one dimensional subspaces of A. Suppose A is a homogeneous algebra over an infinite field k. Let L-a denote left mulfiplication by any nonzero element a is an element of A. Several results are proved concerning the s...

A (non-associative) algebra A, over a field k, is called homogeneous if its automorphism group permutes transitively the one dimensional subspaces of A. Suppose A is a nontrivial finite dimensional homogeneous algebra over an infinite field. Then we prove that x(2) = 0 for all x in A, and so xy = yx...

A matrix M is nilpotent of index 2 if M2=0. Let V be a space of nilpotent n×n matrices of index 2 over a field k where and suppose that r is the maximum rank of any matrix in V. The object of this paper is to give an elementary proof of the fact that . We show that the inequality is sharp and const...