Some Characterizations of Upper Semimodular Lattices and Posets

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Authors

  • R. S. Shewale
     Sinhgad College of Engineering, Pune 411 041 ,IN
  • Vilas Kharat
     Department of Mathematics, Savitribai Phule Pune University, Pune 411 007 ,IN

Keywords:

Semimodular Lattice, Poset, Mac Lane Conditions, M-Symmetry.
Lattices

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.

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Published

2015-12-01

How to Cite

Shewale, R. S., & Kharat, V. (2015). Some Characterizations of Upper Semimodular Lattices and Posets. The Journal of the Indian Mathematical Society, 82(3-4), 189–205. Retrieved from https://informaticsjournals.com/index.php/jims/article/view/1693

Issue

Volume 82, Issue 3-4, July-December 2015

Section

Articles

License

Copyright (c) 2015 R. S. Shewale, Vilas Kharat

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

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