%0 Journal Article 
%A Pardo Espino, Enrique
%T Comparability, Separativity, and exchange rings
%D 1996
%@ 0092-7872
%U http://hdl.handle.net/10498/16079
%X There are several long-standing open problems which ask whether
regular rings, and C -algebras of real rank zero, satisfy certain module
cancellation properties. Ara, Goodearl, O'Meara and Pardo recently
observed that both types of rings are exchange rings, and showed that
separative exchange rings have these good cancellation properties, thus
answering the questions a rmatively in the separative case. In this ar-
ticle, we prove that, for any positive integer s, exchange rings satisfying
s-comparability are separative, thus answering the questions a rma-
tively in the s-comparable case.
We also introduce the weaker, more technical, notion of generalized
s-comparability, and show that this condition still implies separativity
for exchange rings. On restricting to directly  nite regular rings, we
recover results of Ara, O'Meara and Tyukavkin.
%~ Universidad de Cádiz