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Neeman's characterization of K(R-Proj) via Bousfield localization
- Source :
- Journal of Pure and Applied Algebra. 222:2288-2291
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
Abstract
- Let $R$ be an associative ring with unit and denote by $K({\rm R \mbox{-}Proj})$ the homotopy category of complexes of projective left $R$-modules. Neeman proved the theorem that $K({\rm R \mbox{-}Proj})$ is $\aleph_1$-compactly generated, with the category $K^+ ({\rm R \mbox{-}proj})$ of left bounded complexes of finitely generated projective $R$-modules providing an essentially small class of such generators. Another proof of Neeman's theorem is explained, using recent ideas of Christensen and Holm, and Emmanouil. The strategy of the proof is to show that every complex in $K({\rm R \mbox{-}Proj})$ vanishes in the Bousfield localization $K({\rm R \mbox{-}Flat})/\langle K^+ ({\rm R \mbox{-}proj}) \rangle.$<br />Comment: 5 pages
- Subjects :
- Ring (mathematics)
Algebra and Number Theory
Homotopy category
010102 general mathematics
Mathematics - Rings and Algebras
Characterization (mathematics)
01 natural sciences
16E05, 18E30, 18G35, 55U15
Combinatorics
Proj construction
Rings and Algebras (math.RA)
Small class
Bounded function
0103 physical sciences
FOS: Mathematics
010307 mathematical physics
Representation Theory (math.RT)
0101 mathematics
Unit (ring theory)
Mathematics - Representation Theory
Mathematics
Bousfield localization
Subjects
Details
- ISSN :
- 00224049
- Volume :
- 222
- Database :
- OpenAIRE
- Journal :
- Journal of Pure and Applied Algebra
- Accession number :
- edsair.doi.dedup.....5ae1ce23dab1b3ff74a58ed5876cfa0e