Pseudo-BCH Semilattices

Andrzej Walendziak

Bulletin of the Section of Logic (2018)

  • Volume: 47, Issue: 2
  • ISSN: 0138-0680

Abstract

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In this paper we study pseudo-BCH algebras which are semilattices or lattices with respect to the natural relations ≤; we call them pseudo-BCH join-semilattices, pseudo-BCH meet-semilattices and pseudo-BCH lattices, respectively. We prove that the class of all pseudo-BCH join-semilattices is a variety and show that it is weakly regular, arithmetical at 1, and congruence distributive. In addition, we obtain the systems of identities defininig pseudo-BCH meet-semilattices and pseudo-BCH lattices.

How to cite

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Andrzej Walendziak. "Pseudo-BCH Semilattices." Bulletin of the Section of Logic 47.2 (2018): null. <http://eudml.org/doc/295525>.

@article{AndrzejWalendziak2018,
abstract = {In this paper we study pseudo-BCH algebras which are semilattices or lattices with respect to the natural relations ≤; we call them pseudo-BCH join-semilattices, pseudo-BCH meet-semilattices and pseudo-BCH lattices, respectively. We prove that the class of all pseudo-BCH join-semilattices is a variety and show that it is weakly regular, arithmetical at 1, and congruence distributive. In addition, we obtain the systems of identities defininig pseudo-BCH meet-semilattices and pseudo-BCH lattices.},
author = {Andrzej Walendziak},
journal = {Bulletin of the Section of Logic},
keywords = {(pseudo-)BCK/BCI/BCH algebra; pseudo-BCH join (meet)-semilattice; weakly regular; arithmetical at 1},
language = {eng},
number = {2},
pages = {null},
title = {Pseudo-BCH Semilattices},
url = {http://eudml.org/doc/295525},
volume = {47},
year = {2018},
}

TY - JOUR
AU - Andrzej Walendziak
TI - Pseudo-BCH Semilattices
JO - Bulletin of the Section of Logic
PY - 2018
VL - 47
IS - 2
SP - null
AB - In this paper we study pseudo-BCH algebras which are semilattices or lattices with respect to the natural relations ≤; we call them pseudo-BCH join-semilattices, pseudo-BCH meet-semilattices and pseudo-BCH lattices, respectively. We prove that the class of all pseudo-BCH join-semilattices is a variety and show that it is weakly regular, arithmetical at 1, and congruence distributive. In addition, we obtain the systems of identities defininig pseudo-BCH meet-semilattices and pseudo-BCH lattices.
LA - eng
KW - (pseudo-)BCK/BCI/BCH algebra; pseudo-BCH join (meet)-semilattice; weakly regular; arithmetical at 1
UR - http://eudml.org/doc/295525
ER -

References

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  5. [5] G. Georgescu, A. Iorgulescu, Pseudo-BL algebras: a noncommutative extension of BL algebras, [in:] Abstracts of the Fifth International Conference FSTA 2000 (Slovakia, February 2000), pp. 90–92. 
  6. [6] G. Georgescu, A. Iorgulescu, Pseudo-BCK algebras: an extension of BCK algebras, [in:] Proc. of DMTCS’01: Combinatorics, Computability and Logic (Springer, London, 2001), pp. 97–114. 
  7. [7] Q. P. Hu, X. Li, On BCH-algebras, Mathematics Seminar Notes 11 (1983), pp. 313–320. 
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  9. [9] A. Iorgulescu, New generalizations of BCI, BCK and Hilbert algebras – Part I, Journal of Multiple-Valued Logic and Soft Computing 27 (2016), pp. 353–406. 
  10. [10] A. Iorgulescu, New generalizations of BCI, BCK and Hilbert algebras – Part II, Jornal of Multiple-Valued Logic and Soft Computing 27 (2016), pp. 407–456. 
  11. [11] K. Iséki, An algebra related with a propositional culculus, Proceedings of the Japan Academy 42 (1966), pp. 26–29. 
  12. [12] K. Iséki, S. Tanaka, An introduction to the theory of BCK-algebra, Mathematica Japonica 23 (1978), pp. 1–26. 
  13. [13] J. Kühr, Pseudo BCK-semilattices, Demonstratio Mathematica 40 (2007), pp. 495–516. 
  14. [14] A. Walendziak, Pseudo-BCH-algebras, Discussiones Mathematicae – General Algebra and Applications 35 (2015), pp. 1–15. 
  15. [15] A. Walendziak, On ideals of pseudo-BCH-algebras, Annales Universitatis Mariae Curie-Skłodowska, Sectio A, Mathematica, 70 (2016), pp. 81–91. 

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