(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, firstly, we give characterizations of filters in implicative negatively partially ordered ternary semigroups and in commutative implicative negatively partially ordered ternary semigroups. Secondly, we introduce the notion of implicative filters of implicative negatively partially ordered ternary semigroups; an example is established. We show that every implicative filter is a filter and give an example to show that the converse is not true in general. Finally, we state some equivalent conditions for an implicative filter by using a particular set defined by a filter.