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Algebra Logika, 2019, Volume 58, Number 4, Pages 500–511 (Mi al912)  

Asymptotic rank theorems

K. V. Storozhuk

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: Let $A$ be a numerical $k\times\infty$-matrix such that minors $A_I$ of order $k$ tend to zero if numbers of all columns forming these minors tend to infinity. It is shown that there exits a nontrivial linear combination of rows in $A$ which is a sequence tending to zero.

Keywords: $k\times\infty$-matrix, asymptotic rank.

DOI: https://doi.org/10.33048/alglog.2019.58.406

Full text: PDF file (164 kB)
First page: PDF file

English version:
Algebra and Logic, 2019, 58:4, 337–344

Bibliographic databases:

UDC: 512.64
Received: 17.11.2018
Revised: 08.11.2019

Citation: K. V. Storozhuk, “Asymptotic rank theorems”, Algebra Logika, 58:4 (2019), 500–511; Algebra and Logic, 58:4 (2019), 337–344

Citation in format AMSBIB
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\by K.~V.~Storozhuk
\paper Asymptotic rank theorems
\jour Algebra Logika
\yr 2019
\vol 58
\issue 4
\pages 500--511
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\crossref{https://doi.org/10.33048/alglog.2019.58.406}
\transl
\jour Algebra and Logic
\yr 2019
\vol 58
\issue 4
\pages 337--344
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