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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 Kgroup K1(R)=GL(R)/E(R) of R, giving an elementary description that does not involve elementary matrices explicitly.
Original language  English 

Pages (fromto)  79 
Number of pages  4 
Journal  Algebra and Discrete Mathematics 
Volume  30 
Issue number  1 
Early online date  01 Jun 2020 
DOIs  
Publication status  Early online date  01 Jun 2020 
ASJC Scopus subject areas
 Algebra and Number Theory
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