Thakare, N. K.; Maeda, S.; Waphare, B. N. Modular pairs, covering property and related results in posets. (English) Zbl 1117.06300 J. Indian Math. Soc., New Ser. 70, No. 1-4, 229-253 (2003). Summary: How should one define a modular pair in a general poset? This question was raised by Birkhoff sixty years ago. Not only answer we this open problem satisfactorily, but we, moreover, obtain interesting properties concerning covering property and 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, orthomodular posets are also characterized and an interesting open problem in this context is raised. Cited in 7 Documents MSC: 06A06 Partial orders, general 06A11 Algebraic aspects of posets 06A12 Semilattices 06C05 Modular lattices, Desarguesian lattices 06C15 Complemented lattices, orthocomplemented lattices and posets Keywords:poset; upper (lower) cone; semilattice; lattice; covering relation; atom; modular pair; covering property; exchange property; del-relation; perspectivity; atom space; orthomodular posets PDFBibTeX XMLCite \textit{N. K. Thakare} et al., J. Indian Math. Soc., New Ser. 70, No. 1--4, 229--253 (2003; Zbl 1117.06300)