On two classes of pseudo-BCI-algebras

Grzegorz Dymek

Discussiones Mathematicae - General Algebra and Applications (2011)

  • Volume: 31, Issue: 2, page 217-174
  • ISSN: 1509-9415

Abstract

top
The class of p-semisimple pseudo-BCI-algebras and the class of branchwise commutative pseudo-BCI-algebras are studied. It is proved that they form varieties. Some congruence properties of these varieties are displayed.

How to cite

top

Grzegorz Dymek. "On two classes of pseudo-BCI-algebras." Discussiones Mathematicae - General Algebra and Applications 31.2 (2011): 217-174. <http://eudml.org/doc/276718>.

@article{GrzegorzDymek2011,
abstract = {The class of p-semisimple pseudo-BCI-algebras and the class of branchwise commutative pseudo-BCI-algebras are studied. It is proved that they form varieties. Some congruence properties of these varieties are displayed.},
author = {Grzegorz Dymek},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {pseudo-BCI-algebra; p-semisimplicity; branchwise commutativity; branchwise commutative BCI-algebra},
language = {eng},
number = {2},
pages = {217-174},
title = {On two classes of pseudo-BCI-algebras},
url = {http://eudml.org/doc/276718},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Grzegorz Dymek
TI - On two classes of pseudo-BCI-algebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2011
VL - 31
IS - 2
SP - 217
EP - 174
AB - The class of p-semisimple pseudo-BCI-algebras and the class of branchwise commutative pseudo-BCI-algebras are studied. It is proved that they form varieties. Some congruence properties of these varieties are displayed.
LA - eng
KW - pseudo-BCI-algebra; p-semisimplicity; branchwise commutativity; branchwise commutative BCI-algebra
UR - http://eudml.org/doc/276718
ER -

References

top
  1. [1] W.A. Dudek and Y.B. Jun, Pseudo-BCI algebras, East Asian Math. J. 24 (2008), 187-190. Zbl1149.06010
  2. [2] G. Dymek, Atoms and ideals of pseudo-BCI-algebras, submitted. Zbl1294.06021
  3. [3] G. Dymek, On compatible deductive systems of pseudo-BCI-algebras, submitted. 
  4. [4] G. Dymek, p-semisimple pseudo-BCI-algebras, J. Mult.-Val. Log. Soft Comput., to appear. 
  5. [5] G. Dymek and A. Kozanecka-Dymek, Pseudo-BCI-logic, submitted. 
  6. [6] G. Georgescu and A. Iorgulescu, Pseudo-BCK algebras: an extension of BCK-algebras, Proceedings of DMTCS'01: Combinatorics, Computability and Logic, Springer, London, 2001, 97-114. Zbl0986.06018
  7. [7] G. Georgescu and A. Iorgulescu, Pseudo-BL algebras: a noncommutative extension of BL-algebras, Abstracts of The Fifth International Conference FSTA 2000, Slovakia, February 2000, 90-92. 
  8. [8] G. Georgescu and A. Iorgulescu, Pseudo-MV algebras: a noncommutative extension of MV-algebras, The Proceedings The Fourth International Symposium on Economic Informatics, INFOREC Printing House, Bucharest, Romania, May (1999), 961-968. Zbl0985.06007
  9. [9] A. Iorgulescu, Algebras of logic as BCK algebras, Editura ASE, Bucharest, 2008. 
  10. [10] K. Iséki, An algebra related with a propositional calculus, Proc. Japan. Academy 42 (1966), 26-29. doi: 10.3792/pja/1195522171 Zbl0207.29304
  11. [11] Y.B. Jun, H.S. Kim and J. Neggers, On pseudo-BCI ideals of pseudo BCI-algebras, Mat. Vesnik 58 (2006), 39-46. Zbl1119.03068
  12. [12] K.J. Lee and C.H. Park, Some ideals of pseudo-BCI algebras, J. Appl. Math. & Informatics 27 (2009), 217-231. 
  13. [13] A. Wroński, BCK-algebras do not form a variety, Math. Japon. 28 (1983), 211-213. Zbl0518.06014

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.