Missouri Journal of Mathematical Sciences

Shift Up-Filters and Decompositions of Up-Filters in Up-Algebras

Young Bae Jun and Aiyared Iampan

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Abstract

The decomposition of a UP-filter is first discussed, and then the notion of a shift UP-filter is introduced, and several properties are investigated. Relations between a UP-filter, a comparative UP-filter, and a shift UP-filter are considered. Conditions for a UP-filter to be a shift UP-filter, and for a comparative UP-filter to be a shift UP-filter are provided. Characterizations of a shift UP-filter are considered, and an extension property for a shift UP-filter is established.

Article information

Source
Missouri J. Math. Sci., Volume 31, Issue 1 (2019), 36-45.

Dates
First available in Project Euclid: 30 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1559181624

Digital Object Identifier
doi:10.35834/mjms/1559181624

Mathematical Reviews number (MathSciNet)
MR3960285

Subjects
Primary: 03G25: Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35]
Secondary: 06F35: BCK-algebras, BCI-algebras [See also 03G25]

Keywords
UP-algebra (implicative, comparative, shift) UP-filter

Citation

Jun, Young Bae; Iampan, Aiyared. Shift Up-Filters and Decompositions of Up-Filters in Up-Algebras. Missouri J. Math. Sci. 31 (2019), no. 1, 36--45. doi:10.35834/mjms/1559181624. https://projecteuclid.org/euclid.mjms/1559181624


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References

  • A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Top., 5.1 (2017), 35–54.
  • C. Prabpayak and U. Leerawat, On ideals and congruences in KU-algebras, Scientia Magna, 5.1 (2009), 54–57.
  • J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, and A. Iampan, Fuzzy sets in UP-algebras, Annal. Fuzzy Math. Inform., 12.6 (2016), 739–756.