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Direct sum decompositions of modules, almost trace ideals, and pullbacks of monoids
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Published/Copyright:
May 18, 2006
Abstract
We show that a number of pullback diagrams appear naturally in the study of preordered Grothendieck groups. The passage of projective modules from a ring R to a factor ring R/I turns out to be particularly good for a certain class of ideals, which we call almost trace ideals. We generalize to arbitrary rings a result by Goodearl concerning the lattice of the directed convex subgroups of K0(R). Finally, we show that a variant
(I) of the Grothendieck group of I, introduced by Quillen, has an easy description in terms of projective modules when I is an almost trace ideal.
Received: 2004-02-02
Revised: 2004-07-14
Published Online: 2006-05-18
Published in Print: 2006-05-01
© Walter de Gruyter
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Articles in the same Issue
- Measurable metrics and Gaussian concentration
- Direct sum decompositions of modules, almost trace ideals, and pullbacks of monoids
- Spherical means on compact locally symmetric spaces of non-positive curvature
- Reflections acting efficiently on a building
- Decay rates of oscillatory integral operators in “1 + 2” dimensions
- Singular perturbation for the first eigenfunction and blow-up analysis
- Tiles with no spectra
- Pointwise estimates for a model problem in nonlinear elasticity
