Download PDF - Pseudo-BCH-algebrasAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Pseudo-BCH-algebras

Authors 1

Affiliations

  1. Institute of Mathematics and Physics, Siedlce University, 3 Maja 54, 08-110 Siedlce, Poland

Abstract

The notion of pseudo-BCH-algebras is introduced, and some of their properties are investigated. Conditions for a pseudo-BCH-algebra to be a pseudo-BCI-algebra are given. Ideals and minimal elements in pseudo-BCH-algebras are considered.

Keywords

ENG
(pseudo-)BCK/BCI/BCH-algebra, minimal element, (closed) ideal, centre

Bibliography

  1. R.A. Borzooei, A.B. Saeid, A. Rezaei, A. Radfar and R. Ameri, On pseudo-BE-algebras, Discuss. Math. General Algebra and Appl. 33 (2013) 95-97. doi: 10.7151/dmgaa.1193
  2. M.A. Chaudhry, On BCH-algebras, Math. Japonica 36 (1991) 665-676.
  3. W.A. Dudek and Y.B. Jun, Pseudo-BCI-algebras, East Asian Math. J. 24 (2008) 187-190.
  4. G. Dymek, Atoms and ideals of pseudo-BCI-algebras, Comment. Math. 52 (2012) 73-90.
  5. G. Dymek, p-semisimple pseudo-BCI-algebras, J. Mult.-Valued Logic Soft Comput. 19 (2012) 461-474.
  6. G. Georgescu and A. Iorgulescu, Pseudo-MV algebras: a noncommutative extension of MV algebras, in: The Proc. of the Fourth International Symp. on Economic Informatics (Bucharest, Romania, May 1999) 961-968.
  7. G. Georgescu and A. Iorgulescu, Pseudo-BL algebras: a noncommutative extension of BL algebras, in: Abstracts of the Fifth International Conference FSTA 2000 (Slovakia, February, 2000) 90-92.
  8. G. Georgescu and A. Iorgulescu, Pseudo-BCK algebras: an extension of BCK algebras, in: Proc. of DMTCS'01: Combinatorics, Computability and Logic (Springer, London, 2001) 97-114.
  9. Q.P. Hu and X. Li, On BCH-algebras, Math. Seminar Notes 11 (1983) 313-320.
  10. Y. Imai and K. Iséki, On axiom systems of propositional calculi XIV, Proc. Japan Academy 42 (1966) 19-22.
  11. K. Iséki, An algebra related with a propositional culculus, Proc. Japan Academy 42 (1966) 26-29.
  12. Y.B. Jun, H.S. Kim and J. Neggers, On pseudo-BCI ideals of pseudo-BCI-algebras, Matem. Vesnik 58 (2006) 39-46.
  13. Y.B. Jun, H.S. Kim and J. Neggers, Pseudo-d-algebras, Information Sciences 179 (2009) 1751-1759. doi: 10.1016/j.ins.2009.01.021
  14. Y.H. Kim and K.S. So, On minimality in pseudo-BCI-algebras, Commun. Korean Math. Soc. 27 (2012) 7-13. doi: 10.4134/CKMS.2012.27.1.007
  15. K.J. Lee and Ch.H. Park, Some ideals of pseudo-BCI-algebras, J. Appl. & Informatics 27 (2009) 217-231.
  16. J. Neggers and H.S. Kim, On d-algebras, Math. Slovaca 49 (1999) 19-26.
  17. A.B. Saeid and A. Namdar, On n-fold ideals in BCH-algebras and computation algorithms, World Applied Sciences Journal 7 (2009) 64-69.
  18. A. Wroński, BCK-algebras do not form a variety, Math. Japon. 28 (1983) 211-213.
Discussiones Mathematicae - General Algebra and Applications
2015/35/1
Export to PBN, Opens in new tab
Pages:
5-19
Main language of publication
English
Received
2013-07-10
Accepted
2014-11-13
Published
2015

DOI: 10.7151/dmgaa.1233

Exact and natural sciences