Some Characterizations of Upper Semimodular Lattices and Posets
Keywords:
Semimodular Lattice, Poset, Mac Lane Conditions, M-Symmetry.Abstract
In this paper, we introduce two new conditions that give a distinctive description of upper semimodularity in finite lattices. Their relations with the existing conditions due to Mac Lane are established. Also, all these conditions for lattices are generalized for posets and relations amongst them are studied. We also give a forbidden structure as a characterization for finite upper semimodular posets. Several counterexamples are constructed.Downloads
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Copyright (c) 2015 R. S. Shewale, Vilas Kharat
This work is licensed under a Creative Commons Attribution 4.0 International License.
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