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Pere Ara, Alberto Facchini

Direct sum decompositions of modules, almost trace ideals, and pullbacks of monoids

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.

Forum Mathematicum, Walter de Gruyter

Print ISSN: 0933-7741
Volume: 18, 05/2006
Pages: 365 - 389

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