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- Fundamental_theorem_of_algebraic_K-theory abstract "In algebra, the fundamental theorem of algebraic K-theory describes the effects of changing the ring of K-groups from a ring R to or . The theorem was first proved by Bass for and was later extended to higher K-groups by Quillen.Let be the algebraic K-theory of the category of finitely generated modules over a noetherian ring R; explicitly, we can take , where is given by Quillen's Q-construction. If R is a regular ring (i.e., has finite global dimension), then the i-th K-group of R. This is an immediate consequence of the resolution theorem, which compares the K-theories of two different categories (with inclusion relation.)For a noetherian ring R, the fundamental theorem states:(i) .(ii) .The proof of the theorem uses the Q-construction. There is also a version of the theorem for the singular case (for ); this is the version proved in Grayson's paper.".
- Fundamental_theorem_of_algebraic_K-theory wikiPageExternalLink Kbook.html.
- Fundamental_theorem_of_algebraic_K-theory wikiPageExternalLink HigherAlgKThyII.pdf.
- Fundamental_theorem_of_algebraic_K-theory wikiPageID "41437935".
- Fundamental_theorem_of_algebraic_K-theory wikiPageRevisionID "596188658".
- Fundamental_theorem_of_algebraic_K-theory subject Category:Algebraic_K-theory.
- Fundamental_theorem_of_algebraic_K-theory subject Category:Mathematical_theorems.
- Fundamental_theorem_of_algebraic_K-theory comment "In algebra, the fundamental theorem of algebraic K-theory describes the effects of changing the ring of K-groups from a ring R to or . The theorem was first proved by Bass for and was later extended to higher K-groups by Quillen.Let be the algebraic K-theory of the category of finitely generated modules over a noetherian ring R; explicitly, we can take , where is given by Quillen's Q-construction. If R is a regular ring (i.e., has finite global dimension), then the i-th K-group of R.".
- Fundamental_theorem_of_algebraic_K-theory label "Fundamental theorem of algebraic K-theory".
- Fundamental_theorem_of_algebraic_K-theory sameAs m.0ztk5wb.
- Fundamental_theorem_of_algebraic_K-theory sameAs Q17015004.
- Fundamental_theorem_of_algebraic_K-theory sameAs Q17015004.
- Fundamental_theorem_of_algebraic_K-theory wasDerivedFrom Fundamental_theorem_of_algebraic_K-theory?oldid=596188658.
- Fundamental_theorem_of_algebraic_K-theory isPrimaryTopicOf Fundamental_theorem_of_algebraic_K-theory.