On KU-Modules Over KU-Algebras

Main Article Content

Moin A. Ansari, Ali N. A. Koam

Abstract

The paper introduces the concept of modules for KU-algebras, named as KU-modules. It presents basic isomorphism theorems for KU-modules and explores their applications, particularly concerning chains of KU-modules. Additionally, it defines and examines exact sequences of KU-modules. The paper discusses various properties of chains of KU-modules and establishes the butterfly lemma in the context of KU-modules.

Article Details

References

  1. H.A.S. Abujabal, A.B. Thaheem, M. Aslam, On Actions of BCK-Algebras on Groups, Pan Amer. Math. J. 4 (1994), 727–735
  2. A.B. Thaheem, M. Aslam, On Certain Ideals in BCK-Algebras, Math. Japon. 36 (1991), 895–906.
  3. A.H. Hakami, M.A. Ansari, A. Haider, On Some Graphs Based on the Ideals of KU-Algebras, Int. J. Math. Comput. Sci. 19 (2024), 381–394.
  4. R. Giuntini, Quantum MV Algebras, Stud. Logica. 56 (1996), 393–417. https://doi.org/10.1007/bf00372773.
  5. K. Iseki, An Algebra Related With a Propositional Calculus, Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 26–29. https://doi.org/10.3792/pja/1195522171.
  6. C. Prabpayak, U. Leerawat, On Ideals and Congruences in KU-Algebras. Sci. Magna. 5 (2009), 54–57.
  7. C. Prabpayak, U. Leerawat, On Isomorphisms of KU-Algebras, Sci. Magna. 5 (2009), 25–31.
  8. Y. Imai, K. Iseki, on Axiom Systems of Propositional Calculi, XIV, Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 19–22. https://doi.org/10.3792/pja/1195522169.
  9. N. Yaqoob, S.M. Mostafa, M.A. Ansari, On Cubic KU-Ideals of KU-Algebras, ISRN Algebra. 2013 (2013), 935905. https://doi.org/10.1155/2013/935905.
  10. S.M. Mostafa, M.A. Abd-Elnaby and M.M.M. Yousef, Fuzzy Ideals of KU-Algebras, Int. Math. Forum. 6 (2011), 3139–3149.
  11. S.M. Mostafa, M.A. Abd-Elnaby, O.R. Elgendy, Interval Valued Fuzzy KU Ideals in KU-Algebras, Int. Math. Forum, 6 (2011), 3151–3159.
  12. M.A. Ansari, A.N.A. Koam, Rough Approximations in KU-Algebras, Italian J. Pure Appl. Math. 40 (2018), 679–691.
  13. A.N.A. Koam, A. Haider, M.A. Ansari, Pseudo-Metric on KU-Algebras, Korean J. Math. 27 (2019), 131–140. https://doi.org/10.11568/KJM.2019.27.1.131.
  14. T. Senapati, K.P. Shum, Atanassov’s Intuitionistic Fuzzy Bi-Normed KU-Ideals of a KU-Algebra, J. Intell. Fuzzy Syst. 30 (2016), 1169–1180. https://doi.org/10.3233/ifs-151841.