Über Morphismen halbmodularer Verbände |
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Authors: | Ulrich Faigle |
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Institution: | (1) FB Mathematik TH Darmstadt, D-61 Darmstadt, W. Germany |
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Abstract: | Morphisms and weak morphisms extend the concept of strong maps and maps of combinatorial geometry to the class of finite dimensional semimodular lattices. Each lattice which is the image of a semimodular lattice under a morphism is semimodular. In particular, each finite lattice is semimodular if and only if it is the image of a finite distributive lattice under a morphism. Regular and non-singular weak morphisms may be used to characterize modular and distributive lattices. Each morphism gives rise to a geometric closure operator which in turn determines a quotient of a semimodular lattice. A special quotient, the Higgs lift, is constructed and used to show that each morphism decomposes into elementary morphisms, and that each morphism may be factored into an injection and a contraction. |
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Keywords: | Primary 06A15 Secondary 05B35 |
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