Topic
Whitehead problem
About: Whitehead problem is a research topic. Over the lifetime, 47 publications have been published within this topic receiving 969 citations.
Papers
TL;DR: In this paper, the Tannaka-Artin problem was solved, which states the following: is the reduced Whitehead group SK1(A) of a finite-dimensional division algebra A trivial?
Abstract: We solve the old Tannaka-Artin problem, which states the following in modern terminology: is the reduced Whitehead group SK1(A) of a finite-dimensional division algebra A trivial?We work out a method for computing the group SK1(A) based on a reduction to the computation of a group of special protective conorms—a new object in field theory—and we discover unexpected connections with number theory.Bibliography: 25 titles.
66 citations
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TL;DR: It was shown in this paper that for any reasonable ring R, for every R -module K there is a non-projective module M such that Ext R 1 (M, K ) = 0; in particular, there are Whitehead R -modules which are not projective.
55 citations
1 Jan 2008
TL;DR: In this article, the volume conjecture for an infinite family of links called Whitehead chains was proved for generalizing both the Whitehead link and the Borromean rings, which generalizes both the whitehead chain and the BOROMEAN rings.
Abstract: We prove the volume conjecture for an infinite family of links called Whitehead chains that generalizes both the Whitehead link and the Borromean rings.
43 citations
Posted Content•
TL;DR: In this article, direct products of free-abelian and free groups with special emphasis on algorithmic problems are studied, and an explicit expression for an arbitrary endomorphism of a group of arbitrary size is given for the membership problem, isomorphism problem, finite index problem, subgroup and coset intersection problems, the fixed point problem, and the Whitehead problem.
Abstract: We study direct products of free-abelian and free groups with special emphasis on algorithmic problems. After giving natural extensions of standard notions into that family, we find an explicit expression for an arbitrary endomorphism of $\ZZ^m \times F_n$. These tools are used to solve several algorithmic and decision problems for $\ZZ^m \times F_n $: the membership problem, the isomorphism problem, the finite index problem, the subgroup and coset intersection problems, the fixed point problem, and the Whitehead problem.
21 citations
TL;DR: In this paper, it was shown that Con (ZFC)→Con(ZFC+for every α < ω 3 there is a superatomic Boolean algebra of width ω and height α.
Abstract: It was proved by Baumgartner and Shelah that Con (ZFC)→Con (ZFC + “there is a superatomic Boolean algebra of width ω and height ω2”). In this paper we improve Baumgartner-Shelah’s theorem, showing that Con (ZFC)→Con (ZFC+“for every α<ω3 there is a superatomic Boolean algebra of width ω and height α”).
21 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2019 | 1 |
| 2017 | 2 |
| 2016 | 2 |
| 2014 | 2 |
| 2013 | 4 |