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Authors
Affiliations
1 13, General Arun Kumar Vaidya Nagar, Off Sakri Road, Dhule-424001, IN
2 Iwaidani 6-333-10, Matsuyama 790, JP
3 Department of Mathematics, University of Pune, Pune-411007, IN
Source
The Journal of the Indian Mathematical Society, Vol 70, No 1-4 (2003), Pagination: 229-253
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.
Keywords
Poset, Upper (Lower) Cone, Semilattice, Lattice, Covering Relation, Atom, Modular Pair, Covering Property, Exchange Property, Del-Relation, Perspectivity, Atom Space, Orthomodular Posets.
