An elementary description of K1(R) without elementary matrices

Thomas Hüttemann, Zuhong Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

Let R be a ring with unit. Passing to the colimit with respect to the standard inclusions GL(n,R)→GL(n+1,R) (which add a unit vector as new last row and column) yields, by definition, the stable linear group GL(R); the same result is obtained, up to isomorphism, when using the `opposite' inclusions (which add a unit vector as new first row and column). In this note it is shown that passing to the colimit along both these families of inclusions simultaneously recovers the algebraic K-group K1(R)=GL(R)/E(R) of R, giving an elementary description that does not involve elementary matrices explicitly.
Original languageEnglish
Pages (from-to)79
Number of pages4
JournalAlgebra and Discrete Mathematics
Volume30
Issue number1
Early online date01 Jun 2020
DOIs
Publication statusEarly online date - 01 Jun 2020

ASJC Scopus subject areas

  • Algebra and Number Theory

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