Geodesic
Enumeration of ideals of exceptional nilpotent matrix algebras
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 166-171

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In well-known enumerations of characteristic ideals of the algebra $NT(n,K)$ of all (lower) niltriangular $n\times n$ matrices over a field $K$ and in related papers for nilpotent matrix groups and rings, the case $|K|=2$ is, as a rule, excluded from consideration; in this case, every ideal is characteristic. We find a formula for the number of all ideals of the algebra $NT(n,K)$ over any finite field $K$.
Keywords: unitriangular group; niltriangular matrix; nilpotent matrix rings; ideal; combinatorial enumerations. 
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V. P. Krivokolesko; V. M. Levchuk. Enumeration of ideals of exceptional nilpotent matrix algebras. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 166-171. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a15/