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On BHK-Algebras

Year 2020, Volume: 2 Issue: 3, 111 - 119, 31.12.2020

Şule Ayar Özbal

Abstract

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.

Keywords

d-algebras quotient algebras derivations

References

  • Reference1 Ates, C. , Frat, A., Quotient of Pseudo d-Algebras, Romanian Journal Of Mathematics and Computer Science,2019, Volume 9, Issue 2, p.113-120.
  • Reference2 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.
  • Reference3 Georgescu, G. , Iorgulescu, A. , Pseudo BCK-algebras: An extension of BCK-algebras, in: Proc. DMTCS01: Combinatorics, Computability and Logics, Springer, London, 2001, pp. 97114.
  • Reference4 Henkin, L. , An algebraic characterization of quanti_ers, Fund. Math. 37 (1950), 63-74.
  • Reference5 Imai, Y. and Iseki, K. , On axiom systems of propositional calculi, Proc. Japan Acad. 42 (1966), 19-22.
  • Reference6 Iseki, K. , On BCI- algebras, Math. Semin. Notes, Kobe Univ. 8 (1980), 125-130.
  • Reference7 Jun Y.B. , Kim H.S. and J. Neggers, Pseudo d-algebras, Information Sciences 179 (2009) 1751-1759.
  • Reference8 Kaya, K. , Prime rings with-derivations, Hacettepe Bulletin of Natural Sciences and Engineering, vol. 16, pp. 63-71, 1988.
  • Reference9 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.
  • Reference10 Neggers, C. and Kim, H. S. , On d algebras, Math. Slovaca, 49 (1999), No. 1, 19-26.

Year 2020, Volume: 2 Issue: 3, 111 - 119, 31.12.2020

Şule Ayar Özbal

Abstract

References

  • Reference1 Ates, C. , Frat, A., Quotient of Pseudo d-Algebras, Romanian Journal Of Mathematics and Computer Science,2019, Volume 9, Issue 2, p.113-120.
  • Reference2 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.
  • Reference3 Georgescu, G. , Iorgulescu, A. , Pseudo BCK-algebras: An extension of BCK-algebras, in: Proc. DMTCS01: Combinatorics, Computability and Logics, Springer, London, 2001, pp. 97114.
  • Reference4 Henkin, L. , An algebraic characterization of quanti_ers, Fund. Math. 37 (1950), 63-74.
  • Reference5 Imai, Y. and Iseki, K. , On axiom systems of propositional calculi, Proc. Japan Acad. 42 (1966), 19-22.
  • Reference6 Iseki, K. , On BCI- algebras, Math. Semin. Notes, Kobe Univ. 8 (1980), 125-130.
  • Reference7 Jun Y.B. , Kim H.S. and J. Neggers, Pseudo d-algebras, Information Sciences 179 (2009) 1751-1759.
  • Reference8 Kaya, K. , Prime rings with-derivations, Hacettepe Bulletin of Natural Sciences and Engineering, vol. 16, pp. 63-71, 1988.
  • Reference9 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.
  • Reference10 Neggers, C. and Kim, H. S. , On d algebras, Math. Slovaca, 49 (1999), No. 1, 19-26.
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Şule Ayar Özbal 0000-0001-5933-5858

Submission Date July 28, 2020
Acceptance Date November 5, 2020
Publication Date December 31, 2020
Published in Issue Year 2020 Volume: 2 Issue: 3

Cite

APA Ayar Özbal, Ş. (2020). On BHK-Algebras. ALKÜ Fen Bilimleri Dergisi, 2(3), 111-119.
AMA Ayar Özbal Ş. On BHK-Algebras. ALKÜ Fen Bilimleri Dergisi. December 2020;2(3):111-119.
Chicago Ayar Özbal, Şule. “On BHK-Algebras”. ALKÜ Fen Bilimleri Dergisi 2, no. 3 (December 2020): 111-19.
EndNote Ayar Özbal Ş (December 1, 2020) On BHK-Algebras. ALKÜ Fen Bilimleri Dergisi 2 3 111–119.
IEEE Ş. Ayar Özbal, “On BHK-Algebras”, ALKÜ Fen Bilimleri Dergisi, vol. 2, no. 3, pp. 111–119, 2020.
ISNAD Ayar Özbal, Şule. “On BHK-Algebras”. ALKÜ Fen Bilimleri Dergisi 2/3 (December2020), 111-119.
JAMA Ayar Özbal Ş. On BHK-Algebras. ALKÜ Fen Bilimleri Dergisi. 2020;2:111–119.
MLA Ayar Özbal, Şule. “On BHK-Algebras”. ALKÜ Fen Bilimleri Dergisi, vol. 2, no. 3, 2020, pp. 111-9.
Vancouver Ayar Özbal Ş. On BHK-Algebras. ALKÜ Fen Bilimleri Dergisi. 2020;2(3):111-9.