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The aim of this work is to show that (oriented) matroid methods can be applied to many discrete geometries, namely those based on modules over integral (ordered) domains. The trick is to emulate the structure of a vector space within the module, thereby allowing matroid methods to be used as if the module were a vector space. Only those submodules which are "closed under existing divisors," and hence behave like vector subspaces, are used as subspaces of the matroid. It is also shown thatdoi:10.1016/s1571-0661(04)80763-1 fatcat:rd3i4xgtovaj5lyjfs7o4swvi4