Research Article
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Year 2021, , 89 - 93, 30.06.2021
https://doi.org/10.47000/tjmcs.789131

Abstract

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.

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

Year 2021, , 89 - 93, 30.06.2021
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.

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.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Daniel A. Romano 0000-0003-1148-3258

Publication Date June 30, 2021
Published in Issue Year 2021

Cite

APA Romano, D. A. (2021). Two Types of Prime UP-Filters of Meet-Commutative UP-Algebras. Turkish Journal of Mathematics and Computer Science, 13(1), 89-93. https://doi.org/10.47000/tjmcs.789131
AMA Romano DA. Two Types of Prime UP-Filters of Meet-Commutative UP-Algebras. TJMCS. June 2021;13(1):89-93. doi:10.47000/tjmcs.789131
Chicago Romano, Daniel A. “Two Types of Prime UP-Filters of Meet-Commutative UP-Algebras”. Turkish Journal of Mathematics and Computer Science 13, no. 1 (June 2021): 89-93. https://doi.org/10.47000/tjmcs.789131.
EndNote Romano DA (June 1, 2021) Two Types of Prime UP-Filters of Meet-Commutative UP-Algebras. Turkish Journal of Mathematics and Computer Science 13 1 89–93.
IEEE D. A. Romano, “Two Types of Prime UP-Filters of Meet-Commutative UP-Algebras”, TJMCS, vol. 13, no. 1, pp. 89–93, 2021, doi: 10.47000/tjmcs.789131.
ISNAD Romano, Daniel A. “Two Types of Prime UP-Filters of Meet-Commutative UP-Algebras”. Turkish Journal of Mathematics and Computer Science 13/1 (June 2021), 89-93. https://doi.org/10.47000/tjmcs.789131.
JAMA Romano DA. Two Types of Prime UP-Filters of Meet-Commutative UP-Algebras. TJMCS. 2021;13:89–93.
MLA Romano, Daniel A. “Two Types of Prime UP-Filters of Meet-Commutative UP-Algebras”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 1, 2021, pp. 89-93, doi:10.47000/tjmcs.789131.
Vancouver Romano DA. Two Types of Prime UP-Filters of Meet-Commutative UP-Algebras. TJMCS. 2021;13(1):89-93.