Generalized \((f_q, h_q)\)-Derivations and Their Structural Role in BP-Algebras

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DOI: https://doi.org/10.28924/2291-8639-23-2025-219
Published: Sep 8, 2025
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Patchara Muangkarn, Innavanh Namkhaluck, Cholatis Suanoom, Aiyared Iampan, Generalized \((f_q, h_q)\)-Derivations and Their Structural Role in BP-Algebras, Int. J. Anal. Appl., 23 (2025), 219.

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Patchara Muangkarn, Innavanh Namkhaluck, Cholatis Suanoom, Aiyared Iampan

Abstract

This paper introduces and investigates the concept of (fq, hq)-derivations in BP-algebras, extending the existing framework of fq-derivations by incorporating two endomorphisms and a fixed element. We formally define inside and outside (fq, hq)-derivations, as well as left-right and right-left variants, and establish several algebraic properties characterizing their behavior. Illustrative examples are provided to demonstrate their validity and distinguish them from classical derivations. Fundamental theorems are proved, including regularity conditions, identity behavior, and commutative properties of the involved endomorphisms. These results not only generalize previous findings but also enhance the theoretical understanding of non-classical derivations in algebraic structures, with potential implications for logic, fuzzy computation, and information systems.

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References

  1. S.S. Ahn, J.S. Han, On BP-Algebras, Hacettepe J. Math. Stat. 42 (2013), 551–557.
  2. N.O. Al-Shehrie, Derivations of B-Algebras, J. King Abdulaziz Univ. - Sci. 22 (2010), 71–83.
  3. L.K. Ardekani, B. Davvaz, On $(f, g)$-Derivations of B-Algebras, Mat. Vesnik 66 (2014), 125–132.
  4. M. Ashraf, S. Ali, C. Haetinger, On Derivations in Rings and Their Applications, Aligarh Bull. Math. 25 (2006), 79–107.
  5. T. Bantaojai, C. Suanoom, J. Phuto, A. Iampan, A Bi-Endomorphism Induces a New Type of Derivations on B-Algebras, Ital. J. Pure Appl. Math. 48 (2022), 336–348.
  6. S. Gemawati, Mashadi, M. M, E. Fitria, $fq$-derivation of $BP$-Algebras, J. Indones. Math. Soc. 29 (2023), 235–244. https://doi.org/10.22342/jims.29.2.1448.235-244.
  7. A. Iampan, N. Rajesh, C. Arivazhagi, R. Vennila, Structural Derivations in Hilbert Algebras by Endomorphisms, Int. J. Anal. Appl. 22 (2024), 213. https://doi.org/10.28924/2291-8639-22-2024-213.
  8. H.S. Kim, H.G. Park, On $0$-Commutative B-Algebras, Sci. Math. Jpn. Online e-2005 (2005), 31–36.
  9. P. Muangkarn, C. Suanoom, A. Iampan, New Derivations of $d$-Algebras Based on Endomorphisms, Int. J. Math. Comput. Sci. 17 (2022), 1025–1032.
  10. P. Muangkarn, C. Suanoom, P. Pengyim, A. Iampan, $fq$-Derivations of $b$-Algebras, J. Math. Comput. Sci. 11 (2021), 2047–2057. https://doi.org/10.28919/jmcs/5472.
  11. J. Neggers, H.S. Kim, On B-Algebras, Mat. Vesnik 54 (2002), 21–29.
  12. K. Sawika, R. Intasan, A. Kaewwasri, A. Iampan, Derivations of UP-Algebras, Korean J. Math. 24 (2016), 345–367. https://doi.org/10.11568/KJM.2016.24.3.345.