# On two classes of pseudo-BCI-algebras

Discussiones Mathematicae - General Algebra and Applications (2011)

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

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topGrzegorz 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] W.A. Dudek and Y.B. Jun, Pseudo-BCI algebras, East Asian Math. J. 24 (2008), 187-190. Zbl1149.06010
- [2] G. Dymek, Atoms and ideals of pseudo-BCI-algebras, submitted. Zbl1294.06021
- [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. Zbl0986.06018
- [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. Zbl0985.06007
- [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 Zbl0207.29304
- [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] 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. Zbl0518.06014

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