A decomposition theorem for CK1 of central simple algebras

Roozbeh Hazrat; Robert Wilson

doi:10.1080/00927870600936716

A decomposition theorem for CK₁ of central simple algebras

Roozbeh Hazrat
, Robert Wilson

Queen's University Belfast

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let A be a central simple algebra over its center F. Define CK₁A = Coker(K₁F → K₁A). We prove that if A and B are F-central simple algebras of coprime degrees, then CK₁(A ⊗ _FB) = CK₁A × CK₁B.

Original language	English
Pages (from-to)	4573-4578
Number of pages	6
Journal	Communications in Algebra
Volume	34
Issue number	12
DOIs	https://doi.org/10.1080/00927870600936716
Publication status	Published - 1 Dec 2006
Externally published	Yes

Keywords

Central simple algebras
Division algebras
Reduced K-theory

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10.1080/00927870600936716

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title = "A decomposition theorem for CK1 of central simple algebras",

abstract = "Let A be a central simple algebra over its center F. Define CK1A = Coker(K1F → K1A). We prove that if A and B are F-central simple algebras of coprime degrees, then CK1(A ⊗ FB) = CK1A × CK1B.",

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AU - Wilson, Robert

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N2 - Let A be a central simple algebra over its center F. Define CK1A = Coker(K1F → K1A). We prove that if A and B are F-central simple algebras of coprime degrees, then CK1(A ⊗ FB) = CK1A × CK1B.

AB - Let A be a central simple algebra over its center F. Define CK1A = Coker(K1F → K1A). We prove that if A and B are F-central simple algebras of coprime degrees, then CK1(A ⊗ FB) = CK1A × CK1B.

KW - Central simple algebras

KW - Division algebras

KW - Reduced K-theory

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DO - 10.1080/00927870600936716

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VL - 34

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JF - Communications in Algebra

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ER -

A decomposition theorem for CK₁ of central simple algebras

Abstract

Keywords

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