Abstract
AbstractIn his fundamental paper on group cohomology [20] R.G. Swan defined a homomorphism for any finite group G which, in this restricted context, has since been used extensively both in the classification of projective modules and the algebraic homotopy theory of finite complexes ([3], [18], [21]). We extend the definition so that, for suitable modules J over reasonably general rings Λ, it takes the form here is the quotient of the category of Λ-homomorphisms obtained by setting ‘projective = 0’. We then employ it to give an exact classification of homotopy classes of extensions 0 → J → Fn → … → F0 → F0 → M → 0 where each Fr is finitely generated free.
Publisher
Cambridge University Press (CUP)
Subject
Geometry and Topology,Algebra and Number Theory
Reference24 articles.
1. On the Swan subgroup of certain periodic groups
2. On the homotopy types of certain two-dimensional complexes;Cockroft;Proc. L. M. S.,1961
3. Skew Fields
4. Groups with homological duality
Cited by
1 articles.
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