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Journal of the Ramanujan Mathematical Society

Volume 36, Issue 4, December 2021  pp. 301–307.

Frankl's conjecture and lattices derived from reduced semigroups

Authors:  Vinayak Joshi
Author institution:Department of Mathematics, Savitribai Phule Pune University, Pune 411 007, Maharashtra, India

Summary:  In this paper, we prove Frankl's Conjecture for the class of lattices (a subclass of 0-distributive lattices) derived from reduced semigroups, which satisfies the annihilator condition. A new conjecture is introduced for the class of 0-distributive lattices which implies Frankl's Conjecture. Also, we observe that the class of multiplicative lattices also satisfies Frankl's Conjecture.

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