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Archiv der Mathematik

, Volume 86, Issue 4, pp 317–320 | Cite as

Grothendieck groups of unbounded complexes of finitely generated modules

  • Jun-ichi Miyachi
Original Paper

Abstract.

Let Λ be a left Artinian ring, D+(mod Λ) (resp., D(mod Λ), D(mod Λ)) the derived category of bounded below complexes (resp., bounded above complexes, unbounded complexes) of finitely generated left Λ-modules. We show that the Grothendieck groups K 0(D+(mod Λ)), K 0(D(mod Λ)) and K 0(D(mod Λ)) are trivial.

Mathematics Subject Classification (2000).

16E30 16G10 18E30 18F30 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of MathematicsTokyo Gakugei UniversityTokyoJapan

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