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ArticleOriginal scientific text

Title

On two classes of pseudo-BCI-algebras

Authors 1

Affiliations

  1. Faculty of Mathematics and Natural Sciences, The John Paul II Catholic University of Lublin, Konstantynów 1H, 20-708 Lublin, Poland

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.

Keywords

ENG
pseudo-BCI-algebra, p-semisimplicity, branchwise commutativity

Bibliography

  1. W.A. Dudek and Y.B. Jun, Pseudo-BCI algebras, East Asian Math. J. 24 (2008), 187-190.
  2. G. Dymek, Atoms and ideals of pseudo-BCI-algebras, submitted.
  3. G. Dymek, On compatible deductive systems of pseudo-BCI-algebras, submitted.
  4. G. Dymek, p-semisimple pseudo-BCI-algebras, J. Mult.-Val. Log. Soft Comput., to appear.
  5. G. Dymek and A. Kozanecka-Dymek, Pseudo-BCI-logic, submitted.
  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.
  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. 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.
  9. A. Iorgulescu, Algebras of logic as BCK algebras, Editura ASE, Bucharest, 2008.
  10. K. Iséki, An algebra related with a propositional calculus, Proc. Japan. Academy 42 (1966), 26-29. doi: 10.3792/pja/1195522171
  11. Y.B. Jun, H.S. Kim and J. Neggers, On pseudo-BCI ideals of pseudo BCI-algebras, Mat. Vesnik 58 (2006), 39-46.
  12. K.J. Lee and C.H. Park, Some ideals of pseudo-BCI algebras, J. Appl. Math. & Informatics 27 (2009), 217-231.
  13. A. Wroński, BCK-algebras do not form a variety, Math. Japon. 28 (1983), 211-213.
Discussiones Mathematicae - General Algebra and Applications
2011/31/2
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Pages:
217-174
Main language of publication
English
Received
2011-06-03
Accepted
2011-07-25
Published
2011

DOI: 10.7151/dmgaa.1184

Exact and natural sciences