1-Modular Dual Nearlattices
Shiuly Akhter, A. S. A. Noor · Annals of Pure and Applied Mathematics · 2018
Jayaram [2] introduced the concept of 0-modular semilattice.Recently, Rahman et al. [4] have introduced the concept of 0-modular Nearlattice.In this paper, we discuss 1-modular dual nearlattice.A dual nearlattice ܵ with 1 is said to be 1-modular if for all ܽ, ܾ, ܿ ∈ ܵ with ܿ ≥ ܽ and ܽ ∨ ܾ = 1 imply ܽ ∨ ሺܾ ∧ ܿሻ = ܿ provided ܾ ∧ ܿ exists.Akhter and Noor [8] have discussed 1-distributive join semilattice.In this paper, we include several characterizations of 1-modular dual nearlattices.