Frontiers of Mathematics in China >

2018 , Vol. 13 >Issue 1: 55 - 66

DOI: https://doi.org/10.1007/s11464-017-0673-9

RESEARCH ARTICLE

Algebraic K-theory of Gorenstein projective modules

  • Ruixin LI ,
  • Miantao LIU ,
  • Nan GAO
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  • Department of Mathematics, Shanghai University, Shanghai 200444, China

Received date: 25 Apr 2017

Accepted date: 07 Nov 2017

Published date: 12 Jan 2018

Copyright

2017 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

We introduce the Gorenstein algebraic K-theory space and the Gorenstein algebraic K-group of a ring, and show the relation with the classical algebraic K-theory space, and also show the ‘resolution theorem’ in this context due to Quillen. We characterize the Gorenstein algebraic K-groups by two different algebraic K-groups and by the idempotent completeness of the Gorenstein singularity category of the ring. We compute the Gorenstein algebraic K-groups along a recollement of the bounded Gorenstein derived categories of CM-finite Gorenstein algebras.

Key words： Frobenius pair; Gorenstein projective module; Gorenstein algebraic K-group; idempotent complete category; recollement

Cite this article

Ruixin LI , Miantao LIU , Nan GAO . Algebraic K-theory of Gorenstein projective modules[J]. Frontiers of Mathematics in China, 2018 , 13(1) : 55 -66 . DOI: 10.1007/s11464-017-0673-9

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