Decomposition of Cones in Modules over Ordered Rings

摘要

A proper cone is prime if it has no non-trivial direct summand. If a cone has a prime decomposition, then it is unique. Under certain chain conditions finite prime decompositions exist. In a wide class of modules- the PFmodules - every non-trivial summand of a cone lies in its boundary. Certain topological and ring theoretic notions arising from the above are studied in detail. Many clarifying examples and applications are given. In particular, some new results on Hermitian matrices are derived. (Author)