A Note on Modular Pairs and Orthomodularity in Posets

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Authors

  • Department of Mathematics, Mangalore University, Mangalagangothri 574 199, Karnataka State ,IN
  • Department of Mathematics, Mangalore University, Mangalagangothri 574 199, Karnataka State ,IN

Keywords:

Upper(Lower)Cone, Modular Pairs, Orthomodular Posets, Strong Posets, Balanced Posets, Join-Irreducible Elements, Meet-Irreducible Elements.

Abstract

A negative solution to an open problem posed on modular pairs in orthocomplemented posets is obtained by constructing a counterexample. Some relations between join-irreducible elements and modular pairs are discussed. It is also observed that orthomodular posets of finite length are strong and balanced.