On a class of groups satisfying Bass' conjecture

1998 ◽  
Vol 132 (2) ◽  
pp. 307-330 ◽  
Author(s):  
Ioannis Emmanouil
Keyword(s):  
2018 ◽  
Vol 12 (02) ◽  
pp. 321-356
Author(s):  
Alexander Engel ◽  
Michał Marcinkowski

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.


K-Theory ◽  
2000 ◽  
Vol 19 (3) ◽  
pp. 211-217 ◽  
Author(s):  
James A. Schafer

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

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

1995 ◽  
Vol 37 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Hua-Ping Yu

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.


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

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

1992 ◽  
Vol 67 (1) ◽  
pp. 214-225 ◽  
Author(s):  
James A. Schafer

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