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Abelian subcategories closed under extensions:K-theory and decompositions. (English summary) Comm. Algebra 35 (2007), no. 3, 807–819. A full subcategory W of the category of modules over a ring R is called wide if it is abelian and closed under extensions. In the case where R is a commutative regular coherent ring, the wide subcategories W that consist of finitely presented modules have been classified by Hovey, who showed that these correspond bijectively to certain unions of closed subsets of SpecR. In the paper under review, the author uses Hovey’s classification in order to study the K0-group and examine the existence of Krull-Schmidt type decompositions for such a wide subcategory W. More precisely, the main results of the paper are the following: I. Let R be a commutative regular coherent ring and W a wide subcategory of R-Mod, which consists of finitely presented modules. Then, the group K0(W) is isomorphic with K0(C), where C is the triangulated subcategory of the derived category D(R) consisting of those perfect complexes with homology groups contained in W