Algebraic K-theory of Gorenstein projective modules

doi:10.1007/s11464-017-0673-9

Front. Math. China

2018, Vol. 13

Issue (1) : 55-66 https://doi.org/10.1007/s11464-017-0673-9

RESEARCH ARTICLE

Algebraic K-theory of Gorenstein projective modules

Ruixin LI, Miantao LIU, Nan GAO(

)

Department of Mathematics, Shanghai University, Shanghai 200444, China

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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.

Keywords Frobenius pair Gorenstein projective module Gorenstein algebraic K-group idempotent complete category recollement

Corresponding Author(s): Nan GAO

Issue Date: 12 January 2018

Cite this article:

Ruixin LI,Miantao LIU,Nan GAO. Algebraic K-theory of Gorenstein projective modules[J]. Front. Math. China, 2018, 13(1): 55-66.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0673-9
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I1/55

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