Commun. Korean Math. Soc. 2002 Vol. 17, No. 4, 577-581 Printed December 1, 2002

Woo Lee Kwangju University

Abstract : The incidence matrices corresponding to a nil-algebra of finite index $n$ can be used to determine the nilpotency. We find the smallest positive integer $m$ such that the sum of the incidence matrices $\sum_P \langle n,\, m \rangle^P$ is invertible. In this paper, we give a different proof of the case that the nil-algebra of index $2$ has nilpotency less than or equal to $4$.