Some formulas for the smallest number of generators of finite direct sum of matrix algebras
نویسنده
چکیده
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 ⊕k i=1 Mni(Z) ni may be used as a generating set of any matrix algebra ⊕k i=1 Mni(R) ni where R is an associative ring with a two-sided 1. 2000 MSC: 16S50, 15A30, 15A33, 15A36, 15A30, 16P90
منابع مشابه
Some formulas for the smallest number of generators for finite direct sums of matrix algebras
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 consequenc...
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We obtain an asymptotic upper bound for the minimal 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 obtain an exact formula for the minimal number of generators for a finite direct sum of 2-by-2 matrix algebras with entries in a finite field. As a consequence, we show...
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