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meet-commutative UP-algebra
Open AccessArticle

Prime and irreducible UP-filters of meet-commutative UP-algebras

Annals of Communications in Mathematics 2021

, 4 (2)

, 106-113

DOI: https://doi.org/10.62072/acm.2021.040202

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.
Open AccessArticle

Weakly irreducible UP-filters of meet-commutative UP-algebras

Annals of Communications in Mathematics 2021

, 4 (1)

, 10-16

DOI: https://doi.org/10.62072/acm.2021.040102

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
Open AccessArticle

Prime UP-filter of the third kind in meet-commutative UP-algebras

Annals of Communications in Mathematics 2020

, 3 (3)

, 193-198

DOI: https://doi.org/10.62072/acm.2020.030302

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.