Some formulas for the smallest number of generators for finite direct sums of matrix algebras

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dc.creatorKravchenko, R. V.
dc.creatorPetrenko, B. V.
dc.date2006-11-22
dc.date2007-10-16
dc.date.accessioned2026-07-07T08:36:31Z
dc.date.available2026-07-07T08:36:31Z
dc.descriptionWe obtain an asymptotic upper bound for the smallest number of generators for a finite direct sum of matrix algebras with entries in a finite field. This produces an upper bound for a similar quantity for integer matrix rings. We also obtain an exact formula for the smallest number of generators for a finite direct sum of 2-by-2 matrix algebras with entries in a finite field and as a consequence obtain a formula for a similar quantity for a finite direct sum of 2-by-2 integer matrix rings. We remark that a generating set the ring $\bigoplus_{i=1}^k M_{n_i}(\mathbb{Z})^{n_i}$ may be used as a generating set of any matrix algebra $\bigoplus_{i=1}^k M_{n_i}(R)^{n_i}$ where $R$ is an associative ring with a two-sided 1.
dc.description29 pages. We found the generating function for gen_{m,2}(q), and we added an appendix containing a 2-generator presentation for a finite direct sum of matrix algebras over an infinite field
dc.identifierhttps://arxiv.org/abs/math/0611674
dc.identifierhttp://arxiv.org/abs/math/0611674
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140086
dc.subjectRings and Algebras
dc.subject16S50, 15A30, 15A33, 15A36, 15A30, 16P90
dc.titleSome formulas for the smallest number of generators for finite direct sums of matrix algebras
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