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arXiv · 1901.10714

Factorization by elementary matrices, null-homotopy and products of exponentials for invertible matrices over rings

Evgueni Doubtsov·Frank Kutzschebauch
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Abstract

Let $R$ be a commutative unital ring. A well-known factorization problem is whether any matrix in $\mathrm{SL}_n(R)$ is a product of elementary matrices with entries in $R$. To solve the problem, we use two approaches based on the notion of the Bass stable rank and on construction of a null-homotopy. Special attention is given to the case, where $R$ is a ring or Banach algebra of holomorphic functions. Also, we consider a related problem on representation of a matrix in $\mathrm{GL}_n(R)$ as a product of exponentials.

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Evgueni Doubtsov, Frank Kutzschebauch. 2019-01-30. Factorization by elementary matrices, null-homotopy and products of exponentials for invertible matrices over rings. https://arxiv.org/abs/1901.10714

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