On two classes of pseudo-BCI-algebras

• Autorzy: Grzegorz Dymek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

pseudo-BCI-algebra; p-semisimplicity; branchwise commutativity

Kategorie tematyczne

• 06F35: BCK-algebras, BCI-algebras
• 03G25: Other algebras related to logic

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2011
• Tom: 31
• Numer: 2
• Strony: 217-174

Daty

wydano

2011

otrzymano

2011-06-03

poprawiono

2011-07-25

Twórcy

autor

Grzegorz Dymek

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

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgaa.1184