Výsledky vyhledávání - "Petrenko, B."

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

Autor: Kravchenko, R. V., Petrenko, B. V.

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

Externí odkaz: http://arxiv.org/abs/math/0611674

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On pairs of matrices generating matrix rings and their presentations

Autor: Petrenko, B. V., Sidki, S. N.

Publikováno v: Journal of Algebra, 310 (2007), no. 1, 15--40

Let $M_n(\mathbb{Z})$ the ring of $n$-by-$n$ matrices with integral entries, and $n \geq 2$. This paper studies the set $G_n(\mathbb{Z})$ of pairs $(A,B) \in M_n(\mathbb{Z})^2$ generating $M_n(\mathbb{Z})$ as a ring. We use several presentations of $

Externí odkaz: http://arxiv.org/abs/math/0512186

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On a Theorem of Lenstra and Schoof

Autor: Petrenko, B. V.

Publikováno v: The Quarterly Journal of Mathematics, 55 (2004), no. 2, 203--206.

We give a detailed proof of Theorem 1.15 from a well-known paper "Primitive normal bases for finite fields" by H.W. Lenstra Jr. and R.J. Schoof. We are not aware of any other proofs. Let $L/K$ be a finite-dimensional Galois field extension and $B$ th

Externí odkaz: http://arxiv.org/abs/math/0209106

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