The Journal of the Indian Mathematical Society

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Posets Dismantlable by Doubly Irreducibles


Affiliations
1 Department of Mathematics, P.E.S. Modern College of Arts, Science and Commerce, Shivajinagar, Pune-411005, India
2 Centre for Advanced Study in Mathematics, Department of Mathematics, Savitribai Phule Pune University, Pune-411007, India
     

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In this paper, we introduce the concept of a poset dismantlable by doubly irreducibles. We also introduce the operations, `1-sum' and `2-sum' of posets. Using these operations, we obtain the structure theorem for posets dismantlable by doubly irreducibles, which generalizes the structure theorem for dismantlable lattices.

Keywords

Chain, Lattice, Poset, Doubly irreducible element
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  • Posets Dismantlable by Doubly Irreducibles

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Authors

A. N. Bhavale
Department of Mathematics, P.E.S. Modern College of Arts, Science and Commerce, Shivajinagar, Pune-411005, India
B. N. Waphare
Centre for Advanced Study in Mathematics, Department of Mathematics, Savitribai Phule Pune University, Pune-411007, India

Abstract


In this paper, we introduce the concept of a poset dismantlable by doubly irreducibles. We also introduce the operations, `1-sum' and `2-sum' of posets. Using these operations, we obtain the structure theorem for posets dismantlable by doubly irreducibles, which generalizes the structure theorem for dismantlable lattices.

Keywords


Chain, Lattice, Poset, Doubly irreducible element

References





DOI: https://doi.org/10.18311/jims%2F2021%2F26053