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- W1995343422 abstract "Quillen has constructed a $K$-theory ${K_{ast }}C$ for nice categories, one of which is the category of projective $R$-modules. We construct a theory $K{V_{ast }}C$ for the nice categories parametrized by rings. When applied to projective modules we recover the Karoubi-Villamayor $K$-theory $K{V_{ast }}(R)$. As an application, we show that the Cartan map from ${K_{ast }}(R)$ to ${G_{ast }}(R)$ factors through the groups $K{V_{ast }}(R)$. We also compute $K{V_{ast }}$ for the categories of faithful projectives and Azumaya algebras, generalizing results of Bass." @default.
- W1995343422 created "2016-06-24" @default.
- W1995343422 creator A5088761619 @default.
- W1995343422 date "1981-02-01" @default.
- W1995343422 modified "2023-09-25" @default.
- W1995343422 title "KV-theory of categories" @default.
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- W1995343422 doi "https://doi.org/10.1090/s0002-9947-1981-0626494-7" @default.
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