J-supplemented lattices

In this work, it is defined J-small elements in lattices. J-small elements with small elements relationship and some of its properties were examined. J-supplemented lattices defined using the J-small elements. It is shown that if L is a J-supplemented lattice, then for every n ∈ L quotient sublattice 1/n is also J-supplemented. It is investigated under which conditions J-supplemented elements can be J-supplemented in quotient sublattices. Similarly, the conditions under which the elements J-supplemented in quotient sublattices will be J-complemented in the container lattices are investigated. Some properties and characterizations of J-supplemented lattices have been studied.