Two Types of Prime UP-Filters of Meet-Commutative UP-Algebras

Year 2021, , 89 - 93, 30.06.2021

Daniel A. Romano

https://doi.org/10.47000/tjmcs.789131

Abstract

The concept of meet-commutative UP-algebra was introduced by Sawika et al. in 2016 and the concept of prime filters in such algebras was introduced and analyzed by Muhiuddin, Romano and Jun. In this article, as a continuation of the previous one, we introduce one more type of prime UP-filters in meet-commutative UP-algebras and we analyze the interrelationships of these two types of prime UP-filters.

Keywords

UP-algebra, meet-commutative UP-algebra, prime UP-filter of the first kind, prime UP-filter of the second kind

References

• [1] Graatzer, G., General Lattice Theory, Birkhauser Verlag, 1998.
• [2] Iampan A., A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Topics, 5(1)(2017), 35–54.
• [3] Iampan, A., Songsaeng, M., Muhiuddin, G., Fuzzy duplex UP-algebras, Eur. J. Pure Appl. Math., 13(3)(2020), 459–471.
• [4] Jun, Y.B., Iampan, A., Implicative UP-filters, Afr. Mat., 30(7-8)(2019), 1093–1101.
• [5] Jun, Y.B., Iampan, A., Comparative and allied UP-filters, Lobachevskii J. Math., 40(1)(2019), 60–66.
• [6] Jun, Y.B., Iampan, A., Shift UP-filters and decomposition of UP-filters in UP-algebras, Missouri J. Math. Sci., 31(1)(2019), 36–45.
• [7] Jun, Y.B., Muhiuddin, G., Romano, D.A., Filters in UP-algebras, review and some new reflections, J. Int. Math. Virtual Inst., 11(1)(2021), 35–52.
• [8] Muhiuddin, G., Romano, D.A., Jun, Y.B., Prime and irreducible UP-filters of meet-commutative UP-algebras, Annals of Communications in Mathematics (Submitted).
• [9] Prabpayak, C., Leerawat, U., On ideals and congruences in KU-algebras, Sci. Magna, 5(1)(2009), 54–57.
• [10] Romano, D.A., Proper UP-filters in UP-algebra, Universal Journal of Mathematics and Applications, 1(2)(2018), 98–100.
• [11] Romano, D.A., Some properties of proper UP-filters of UP-algebras, Fundamental Journal of Mathematics and Applications, 1(2)(2018), 109–111.
• [12] Romano, D.A., Jun, Y.B., Weak implicative UP-filters in UP-algebras, Open Journal of Mathematical Sciences (OMS), 4(2020), 442–447.
• [13] Romano, D.A., Prime UP-filter of the third kind in meet-commutative UP-algebras, Annals of Communications in Mathematics (ACM), 3(3)(2020), 193–198.
• [14] Sawika, K., Intasan, R., Kaewwasri, A., Iampan, A., Derivation of UP-algebras, Korean J. Math., 24(3)(2016), 345–367.
• [15] Senapati, T., Muhiuddin, G., Shum, K.P., Representation of UP-algebras in interval-valued intuitionistic fuzzy environment, Ital. J. Pure Appl. Math., 38(2017), 497–518.
• [16] Somjanta, J., Thuekaew, N., Kumpeangkeaw, P., Iampan, A., Fuzzy sets in UP-algebras, Annal. Fuzzy Math. Inform., 12(2016), 739–756.
• [17] Thongarsa, S., Burandate, P., Iampan, A., Some operations of fuzzy sets in UP-algebras with respect to a triangular norm, Annals of Communication in Mathematics, 2(1)(2019), 1–10.