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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 1, Pages 166–171
(Mi timm1152)
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This article is cited in 5 scientific papers (total in 5 papers)
Enumeration of ideals of exceptional nilpotent matrix algebras
V. P. Krivokolesko, V. M. Levchuk Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk
Abstract:
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.
Received: 30.11.2014
Citation:
V. P. Krivokolesko, V. M. Levchuk, “Enumeration of ideals of exceptional nilpotent matrix algebras”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 1, 2015, 166–171
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https://www.mathnet.ru/eng/timm1152 https://www.mathnet.ru/eng/timm/v21/i1/p166
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Abstract page: | 365 | Full-text PDF : | 89 | References: | 60 | First page: | 9 |
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