2006/11/22 by Rostyslav Kravchenko, R. V. Kravchenko, Kravchenko, R. V. +3
Computer Science · Engineering · Mathematics · #15A30 #15A33 #15A36 #16P90 #16S50 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #graph theory and CDMA systems #math.RA #msc:15A30 #msc:15A33 #msc:15A36 #msc:16P90 #msc:16S50
paper · pdf · doi:10.48550/arxiv.math/0611674
29 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
openalex publication_date 2006/11/22 · arxiv created 2007/10/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We 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 \bigoplusi=1k Mni(ℤ)ni may be used as a generating set of any matrix algebra \bigoplusi=1k Mni(R)ni where R is an associative ring with a two-sided 1.