Quotient hyper pseudo BCK-algebras

Habib Harizavi; Tayebeh Koochakpoor; Rajab Ali Boorzoei

Discussiones Mathematicae - General Algebra and Applications (2013)

  • Volume: 33, Issue: 2, page 147-165
  • ISSN: 1509-9415

Abstract

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In this paper, we first investigate some properties of the hyper pseudo BCK-algebras. Then we define the concepts of strong and reflexive hyper pseudo BCK-ideals and establish some relationships among them and the other types of hyper pseudo BCK-ideals. Also, we introduce the notion of regular congruence relation on hyper pseudo BCK-algebras and investigate some related properties. By using this relation, we construct the quotient hyper pseudo BCK-algebra and give some related results.

How to cite

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Habib Harizavi, Tayebeh Koochakpoor, and Rajab Ali Boorzoei. "Quotient hyper pseudo BCK-algebras." Discussiones Mathematicae - General Algebra and Applications 33.2 (2013): 147-165. <http://eudml.org/doc/270358>.

@article{HabibHarizavi2013,
abstract = {In this paper, we first investigate some properties of the hyper pseudo BCK-algebras. Then we define the concepts of strong and reflexive hyper pseudo BCK-ideals and establish some relationships among them and the other types of hyper pseudo BCK-ideals. Also, we introduce the notion of regular congruence relation on hyper pseudo BCK-algebras and investigate some related properties. By using this relation, we construct the quotient hyper pseudo BCK-algebra and give some related results.},
author = {Habib Harizavi, Tayebeh Koochakpoor, Rajab Ali Boorzoei},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {hyper pseudo BCK-algebra; normal hyper pseudo BCK-ideal; quotient hyper pseudo BCK-algebra; hyper pseudo BCK-algebras; hyper pseudo BCK-ideals; regular congruences},
language = {eng},
number = {2},
pages = {147-165},
title = {Quotient hyper pseudo BCK-algebras},
url = {http://eudml.org/doc/270358},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Habib Harizavi
AU - Tayebeh Koochakpoor
AU - Rajab Ali Boorzoei
TI - Quotient hyper pseudo BCK-algebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2013
VL - 33
IS - 2
SP - 147
EP - 165
AB - In this paper, we first investigate some properties of the hyper pseudo BCK-algebras. Then we define the concepts of strong and reflexive hyper pseudo BCK-ideals and establish some relationships among them and the other types of hyper pseudo BCK-ideals. Also, we introduce the notion of regular congruence relation on hyper pseudo BCK-algebras and investigate some related properties. By using this relation, we construct the quotient hyper pseudo BCK-algebra and give some related results.
LA - eng
KW - hyper pseudo BCK-algebra; normal hyper pseudo BCK-ideal; quotient hyper pseudo BCK-algebra; hyper pseudo BCK-algebras; hyper pseudo BCK-ideals; regular congruences
UR - http://eudml.org/doc/270358
ER -

References

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  8. [8] A. Iorgulescu, Classes of Pseudo BCK-algebra-Part I, Journal of Multiple-valued Logic and Soft Computing 12 (2006) 71-130. 
  9. [9] A. Iorgulescu, Classes of Pseudo BCK-algebra-Part II, Journal of Multiple-valued Logic and Soft Computing 12 (2006) 575-629. 
  10. [10] Y. Imai and K. Iseki, On Axiom System of Prepositional Calculi XIV, Proc. Japan Acad. 42 (1996) 26-29. 
  11. [11] Y.B. Jun, M. Kondo and K.H. Kim, Pseudo Ideals of Pseudo BCK-algebras, Sci. Math. Jap. 8 (2003) 87-91. 
  12. [12] Y.B. Jun, M.M. Zahedi, X.L. Xin and R.A. Borzooei, On Hyper BCK-algebra, Italian J. Pure and Appl. Math. 10 (2000) 127-136. Zbl1008.06014
  13. [13] F. Marty, Scu une généralization de la notion de groups, in: 8th Congress Math. (Ed(s)), (Scandinavian, Stockholm, 1934) 45-49. 
  14. [14] Jie Meng and Young Bae Jun, BCK-algebras (Kyung Moon Sa. Co., 1994). 

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