Annals of Communications in Mathematics

AbstractIn this article, we give a number of important properties of meet-commutative UP-algebras. In the class of these UP-algebras, we introduce and analyze the concepts of prime and irreducible UP-filters.

AbstractThe concept of meet-commutative UP-algebras was introduced in 2016 by Sawika et al. Muhiuddin et al. introduced in 2021 the concept of prime UP-filter (of the first kind) and irreducible UP-filter in meet-commutative UP-algebras. Also, it has been shown that any prime UP-filter in such algebras is irreducible. In this paper, we introduce the concept of weakly irreducible UP-filters in such algebras and show that the prime UPfilter is between this and the irreducible UP-filter. Also, we show the possibility that each irreducible UP-filter is a weakly irreducible UP-filter

AbstractUP-algebra was introduced by Iampan 2017 as a generalization of KU-algebra. The concept of meet-commutative UP–algebras was introduced by Sawika et al. In such algebras, the notion of prime UP-filter of the first kind and the notion of prime UP-filter of the second kind are introduced. In this article, as a continuation of the previous two, the concept of prime UP–filters of the third kind was introduced and the relationship between these three types of prime UP-filters was discussed.