Commuting Nilpotent Operators and Maximal Rank

Let X, (X) over tilde be commuting nilpotent matrices over k with nilpotency p(t), where k is an algebraically closed field of positive characteristic p. We show that if X - (X) over tilde is a certain linear combination of products of pairwise commuting nilpotent matrices, then X is of maximal rank if and only if (X) over tilde is of maximal rank.

Citation Formats
S. Öztürk, “Commuting Nilpotent Operators and Maximal Rank,” COMPLEX ANALYSIS AND OPERATOR THEORY, vol. 4, no. 4, pp. 901–904, 2010, Accessed: 00, 2020. [Online]. Available: