Transitive and Absorbent Filters of Implicative Almost Distributive Lattices

Berhanu Assaye Alaba, Mihret Alamneh, Tilahun Mekonnen Munie

Abstract


In this paper, we introduce the concept of transitive and absorbent filters of implicative almost distributive lattices and studied their properties. A necessary and sufficient condition is derived for every filter to become a transitive filter. Some sufficient conditions are also derived for a filter to become a transitive filter. A set of equivalent conditions is obtained for a filter to become an absorbent filter.

Keywords


Implicative almost distributive lattices; transitive filters; absorbent filters

Full Text:

PDF

References


Y. Xu, “Lattice implication algebras,” Journal of Southwest Jiaotong University, vol. 28, no. 1, pp. 20–27, 1993.

Y. Xu, “On filter of lattice implication algebras,” J Fuzzy Math, vol. 1, pp. 251–260, 1993.

Y.-B. Jun, “Implicative filters of lattice implication algebras,” Bulletin of the Korean Mathematical Society, vol. 34, no. 2, pp. 193–198, 1997.

Y. Xu and K. Qin, “Positive implicative and associative filters of lattice implication algebras,” Bulletin-Korean Mathematical Society, vol. 35, pp. 53–62, 1998.

M. S. Rao, “Transitive and absorbent filters of lattice implication algebras,” Journal of applied mathematics & informatics, vol. 32, no. 3_4, pp. 323–330, 2014.

V. Kolluru and B. Bekele, “Implicative algebras,” Momona Ethiopian Journal of Science, vol. 4, no. 1, pp. 90–101, 2012.

U. M. Swamy and G. Rao, “Almost distributive lattices,” Journal of the Australian Mathematical Society, vol. 31, no. 1, pp. 77–91, 1981.

B. A. Alaba, M. Alamneh, and T. Mekonnen, “Implicative almost distributive lattice,” International Journal of Computing Science and Applied Mathematics, vol. 4, no. 1, pp. 19–22, 2018.

B. A. Alaba, M. Alamneh, and T. Mekonnen, “Positive implicative and associative filters of implicative almost distributive lattice,” on communication.

Y. B. Jun, “Fantastic filters of lattice implication algebras,” International Journal of Mathematics and Mathematical Sciences, vol. 24, no. 4, pp. 277–281, 2000.




DOI: http://dx.doi.org/10.12962/j24775401.v4i2.3597

Refbacks

  • There are currently no refbacks.



View My Stats


Creative Commons License
International Journal of Computing Science and Applied Mathematics by Pusat Publikasi Ilmiah LPPM, Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://iptek.its.ac.id/index.php/ijcsam.