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 language | English |
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Pages (from-to) | 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