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Journals / ALKÜ Fen Bilimleri Dergisi / 2020 / Cilt: 2 Sayı: 3

On BHK-Algebras

Şule Ayar Özbal(YASAR UNIVERSITY)0000-0001-5933-5858
Pages
111–119
Publication Date
2020-12-31
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, the concept of derivation on BHK-algebras is defined and the features of the derivations are studied.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, the concept of BHK-algebras that is a generalization of d-algebras is established, and a survey of relations between BHK-algebras and d-algebras is made.
📊
Key Findings & Data:Algebraical properties of BHK-algebras are derived and some discussions on the cases for a BHK-algebra to be a d-algebra is given.
💡
Conclusion & Impact:Also, the concept of derivation on BHK-algebras is defined and the features of the derivations are studied.
🔬Design:Survey & Empirical Study
📍Scope:Comprehensive Sample
⚙️Variables:d-algebras · quotient algebras · derivations

Özet

In this work, the concept of BHK-algebras that is a generalization of d-algebras is established, and a survey of relations between BHK-algebras and d-algebras is made. Algebraical properties of BHK-algebras are derived and some discussions on the cases for a BHK-algebra to be a d-algebra is given. Additionally, twin ideal is given as a new concept and the quotient BHK-algebras is obtained. Also, the concept of derivation on BHK-algebras is defined and the features of the derivations are studied.

🔖

Cite This Article

Özbal, Ş. A. (2020). On BHK-Algebras. ALKÜ Fen Bilimleri Dergisi, Cilt: 2 Sayı: 3, 111–119. https://ajindex.com/articles/1448085

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References (20)

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  12. Bell, H. E., and Kappe, L. C., Rings in which derivations satisfy certain algebraic conditions, Acta Mathematica Hungarica, vol. 53, no. 3-4, pp. 339-346, 1989. https: //doi.org/10.1007/BF01953371.
  13. Georgescu, G., Iorgulescu, A., Pseudo BCK-algebras: An extension of BCK-algebras, in: Proc. DMTCS01: Combinatorics, Computability and Logics, Springer, London, 2001, pp. 97114.
  14. Henkin, L., An algebraic characterization of quanti_ers, Fund. Math. 37 (1950), 63-74.
  15. Imai, Y. and Iseki, K., On axiom systems of propositional calculi, Proc. Japan Acad. 42 (1966), 19-22.
  16. Iseki, K., On BCI- algebras, Math. Semin. Notes, Kobe Univ. 8 (1980), 125-130.
  17. Jun Y.B., Kim H.S. and J. Neggers, Pseudo d-algebras, Information Sciences 179 (2009) 1751-1759.
  18. Kaya, K., Prime rings with-derivations, Hacettepe Bulletin of Natural Sciences and Engineering, vol. 16, pp. 63-71, 1988.
  19. Jun, Y. B., and Xin, X. L., On derivations of BCI-algebras, Information Sciences, vol. 159, no. 3-4, pp. 167 176, 2004. https://doi.org/10.1016/j.ins.2003.03.0019.
  20. Neggers, C. and Kim, H. S., On d algebras, Math. Slovaca, 49 (1999), No. 1, 19-26.