Pseudo-BCH-algebras

Andrzej Walendziak

Discussiones Mathematicae - General Algebra and Applications (2015)

  • Volume: 35, Issue: 1, page 5-19
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Andrzej Walendziak. "Pseudo-BCH-algebras." Discussiones Mathematicae - General Algebra and Applications 35.1 (2015): 5-19. <http://eudml.org/doc/270365>.

@article{AndrzejWalendziak2015,
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.},
author = {Andrzej Walendziak},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {(pseudo-)BCK/BCI/BCH-algebra; minimal element; (closed) ideal; centre},
language = {eng},
number = {1},
pages = {5-19},
title = {Pseudo-BCH-algebras},
url = {http://eudml.org/doc/270365},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Andrzej Walendziak
TI - Pseudo-BCH-algebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2015
VL - 35
IS - 1
SP - 5
EP - 19
AB - 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.
LA - eng
KW - (pseudo-)BCK/BCI/BCH-algebra; minimal element; (closed) ideal; centre
UR - http://eudml.org/doc/270365
ER -

References

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  2. [2] M.A. Chaudhry, On BCH-algebras, Math. Japonica 36 (1991) 665-676. Zbl0733.06008
  3. [3] W.A. Dudek and Y.B. Jun, Pseudo-BCI-algebras, East Asian Math. J. 24 (2008) 187-190. Zbl1149.06010
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  7. [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. [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. Zbl0986.06018
  9. [9] Q.P. Hu and X. Li, On BCH-algebras, Math. Seminar Notes 11 (1983) 313-320. Zbl0579.03047
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  12. [12] Y.B. Jun, H.S. Kim and J. Neggers, On pseudo-BCI ideals of pseudo-BCI-algebras, Matem. Vesnik 58 (2006) 39-46. Zbl1119.03068
  13. [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 Zbl1179.06008
  14. [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 Zbl1244.06008
  15. [15] K.J. Lee and Ch.H. Park, Some ideals of pseudo-BCI-algebras, J. Appl. & Informatics 27 (2009) 217-231. 
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  17. [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. [18] A. Wroński, BCK-algebras do not form a variety, Math. Japon. 28 (1983) 211-213. Zbl0518.06014

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