Modular Pairs, Covering Property and Related Results in Posets
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Keywords:
Poset, Upper (Lower) Cone, Semilattice, Lattice, Covering Relation, Atom, Modular Pair, Covering Property, Exchange Property, Del-Relation, Perspectivity, Atom Space, Orthomodular Posets.Abstract
How should one define a modular pair in a general poset? queried Birkhoff, sixty years ago. Not only we answer this open problem satisfactorily but obtain interesting properties concerning covering property, exchange property in a poset with zero. In this context a few counter examples are also supplied. This general study has led us, as an offshoot, to thirteen characterizations of covering property in a lattice with zero. Del-relation and perspectivity are characterized in posets. The study of atom spaces is extended to posets. Statischness in atomistic posets is characterized. Further, ortho-modular posets are also characterized and an interesting open problem in this context is raised.Downloads
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Published
2003-12-01
How to Cite
Thakare, N. K., Maeda, S., & Waphare, B. N. (2003). Modular Pairs, Covering Property and Related Results in Posets. The Journal of the Indian Mathematical Society, 70(1-4), 229–253. Retrieved from http://informaticsjournals.com/index.php/jims/article/view/21984
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Copyright (c) 2003 N. K. Thakare, S. Maeda, B. N. Waphare
This work is licensed under a Creative Commons Attribution 4.0 International License.