The Journal of the Indian Mathematical Society

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A Note on Modular Pairs and Orthomodularity in Posets


Affiliations
1 Department of Mathematics, Mangalore University Mangalagangothri 574 199, Karnataka State, India
     

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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.

Keywords

Upper(Lower)Cone, Modular Pairs, Orthomodular Posets, Strong Posets, Balanced Posets, Join-Irreducible Elements, Meet-Irreducible Elements.
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  • A Note on Modular Pairs and Orthomodularity in Posets

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Authors

S. P. Bhatta
Department of Mathematics, Mangalore University Mangalagangothri 574 199, Karnataka State, India
H. S. Ramananda
Department of Mathematics, Mangalore University Mangalagangothri 574 199, Karnataka State, India

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.

Keywords


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