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\textbf{Commuting nilpotent operators with maximal rank}
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Semra \"Ozt\"urk Kaptano\u glu

Department of Mathematics, Orta Do\u gu Teknik \"Universitesi, Ankara, T\"rkiye
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\textbf{Abstract}

Let $X$, $\hat{X}$ be  commuting nilpotent matrices over a field $k$ with nilpotency $p^t$. 
We show
that if $X-\hat{X}$ is a certain linear combination of products of commuting nilpotent
matrices, then $X$ is of maximal rank if and only if $\hat{X}$
is of maximal rank.
In the case,  $k$ is an algebraically closed field of positive characteristic $p$ there is an interpretation about module over group algebras.

\textbf{References}

[1] J. F. Carlson, E. Friedlander, J. Pevtsova, Modules of constant Jordan type, J. Reine Angew. Math., 614, 191–234, 2008.

[2] S.\"O. Kaptano\u glu, Commuting Nilpotent Operators and Maximal Rank, Complex Anal. Oper. Theory, 4, 901--904, 2010.
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