MMN-1782
$\beta_*$ relation on lattices
Celil Nebiyev; Hasan Hüseyin Ökten;Abstract
In this paper, we generalize beta star relation on submodules of a module to elements of a complete modular lattice. Let L be a complete modular lattice. We say a,b∈L are beta star equivalent if and only if for each t∈L such that a∨t=1 then b∨t=1 and for each k∈L such that b∨k=1 then a∨k=1, this is equivalent to a∨b≪1/a and a∨b≪1/b. We show that the beta star relation is an equivalence relation. Then, we examine beta star relation on weakly supplemented lattices. Finally, we show that L is weakly supplemented if and only if for every x∈L, x is equivalent to a weak supplement in L.
Vol. 18 (2017), No. 2, pp. 993-999