Geodesic
On two classes of pseudo-BCI-algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 31 (2011) no. 2, pp. 217-174.

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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: pseudo-BCI-algebra, p-semisimplicity, branchwise commutativity 
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Dymek, Grzegorz. On two classes of pseudo-BCI-algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 31 (2011) no. 2, pp. 217-174. http://geodesic.mathdoc.fr/item/DMGAA_2011_31_2_a6/

[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.