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

Doubtsov, Evgueni; Kutzschebauch, Frank (2019). Factorization by elementary matrices, null-homotopy and products of exponentials for invertible matrices over rings. Analysis and mathematical physics, 9(3), pp. 1005-1018. Springer Nature 10.1007/s13324-019-00289-8

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Let R be a commutative unital ring. A well-known factorization problem is whether any matrix in SLₙ(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 GLₙ(R) as a product of exponentials.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Kutzschebauch, Frank

Subjects:

500 Science > 510 Mathematics

ISSN:

1664-2368

Publisher:

Springer Nature

Language:

English

Submitter:

Michel Arthur Bik

Date Deposited:

17 Feb 2020 14:53

Last Modified:

17 Feb 2020 14:53

Publisher DOI:

10.1007/s13324-019-00289-8

ArXiv ID:

1901.10714

BORIS DOI:

10.7892/boris.139931

URI:

https://boris.unibe.ch/id/eprint/139931

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