On a class of groups satisfying Bass' conjecture

1998 ◽  
Vol 132 (2) ◽  
pp. 307-330 ◽  
Author(s):  
Ioannis Emmanouil
Keyword(s):  
Bass Conjecture

scholarly journals Burghelea conjecture and asymptotic dimension of groups

2018 ◽  
Vol 12 (02) ◽  
pp. 321-356
Author(s):  
Alexander Engel ◽  
Michał Marcinkowski
Keyword(s):  
Cyclic Homology ◽  
Asymptotic Dimension ◽  
Group Rings ◽  
Finitely Generated ◽  
Type Formula ◽  
Complex Group ◽  
Bass Conjecture ◽  
Thompson’S Group ◽  
Decomposition Complexity

We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum–Connes conjecture. The Burghelea conjecture implies the Bass conjecture. We state two conjectures about groups of finite asymptotic dimension, which together imply the Burghelea conjecture for such groups. We prove both conjectures for many classes of groups. It is known that the Burghelea conjecture does not hold for all groups, although no finitely presentable counterexample was known. We construct a finitely presentable (even type [Formula: see text]) counterexample based on Thompson’s group [Formula: see text]. We construct as well a finitely generated counterexample with finite decomposition complexity.

The Bass Conjecture and Group von Neumann Algebras

K-Theory ◽  
2000 ◽  
Vol 19 (3) ◽  
pp. 211-217 ◽  
Author(s):  
James A. Schafer
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann ◽  
Bass Conjecture

scholarly journals Whitehead groups and the Bass conjecture

2003 ◽  
Vol 326 (4) ◽  
pp. 723-757 ◽  
Author(s):  
F. Thomas Farrell ◽  
Peter A. Linnell
Keyword(s):  
Bass Conjecture ◽  
Whitehead Groups

ON TWO CLASSES OF GROUPS SATISFYING THE STRONG BASS CONJECTURE

2002 ◽  
Vol 30 (9) ◽  
pp. 4425-4436 ◽  
Author(s):  
Mihalis Sykiotis
Keyword(s):  
Bass Conjecture

scholarly journals On quasi-duo rings

1995 ◽  
Vol 37 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Hua-Ping Yu
Keyword(s):  
Natural Number ◽  
Left Ideal ◽  
Commutative Rings ◽  
Noncommutative Rings ◽  
Perfect Ring ◽  
Maximal Submodule ◽  
Bass Conjecture ◽  
Infinite Sets

Bass [1] proved that if R is a left perfect ring, then R contains no infinite sets of orthogonal idempotents and every nonzero left R-module has a maximal submodule, and asked if this property characterizes left perfect rings ([1], Remark (ii), p. 470). The fact that this is true for commutative rings was proved by Hamsher [12], and that this is not true in general was demonstrated by examples of Cozzens [7] and Koifman [14]. Hamsher's result for commutative rings has been extended to some noncommutative rings. Call a ring left duo if every left ideal is two-sided; Chandran [5] proved that Bass’ conjecture is true for left duo rings. Call a ring R weakly left duo if for every r ε R, there exists a natural number n(r) (depending on r) such that the principal left ideal Rrn(r) is two-sided. Recently, Xue [21] proved that Bass’ conjecture is still true for weakly left duo rings.

scholarly journals The Bass conjecture and growth in groups

2004 ◽  
Vol 100 (1) ◽  
pp. 23-27
Author(s):  
Anders Karlsson ◽  
Markus Neuhauser
Keyword(s):  
Bass Conjecture

A contribution to Bass' conjecture

2004 ◽  
Vol 7 (3) ◽  
Author(s):  
Ioannis Emmanouil ◽  
Inder Bir S. Passi
Keyword(s):  
Bass Conjecture

Relative cyclic homology and the Bass conjecture

1992 ◽  
Vol 67 (1) ◽  
pp. 214-225 ◽  
Author(s):  
James A. Schafer
Keyword(s):  
Cyclic Homology ◽  
Bass Conjecture
Sign in / Sign up

Export Citation Format

Share Document