Unique Reducibility of Subsets of Commutative Topological Groups and Semigroups.
WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS
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As the term is used here, a reduction of a set is a direct sum decomposition into indecomposable summands. The main goal is to find conditions under which reductions are literally unique, but weaker sorts of uniqueness akin to that of the Krull-Schmidt theorem are also considered. The problem of unique reducibility is a classical one in many contexts, but our approach - particular, its exploitation of the key geometric notion of extreme point in conjunction with combinatorial methods involving the refinement property - appears to be new. Special cases of the main result have been obtained by Isbell in studying factorizations of Banach speaces and by Heller in studying stochastic automata.
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