Geodesic
Pseudo-BCH-algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 1, pp. 5-19.

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The notion of pseudo-BCH-algebras is introduced, and some of their properties are investigated. Conditions for a pseudo-BCH-algebra to be a pseudo-BCI-algebra are given. Ideals and minimal elements in pseudo-BCH-algebras are considered.
Keywords: (pseudo-)BCK/BCI/BCH-algebra, minimal element, (closed) ideal, centre 
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Walendziak, Andrzej. Pseudo-BCH-algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 1, pp. 5-19. http://geodesic.mathdoc.fr/item/DMGAA_2015_35_1_a0/

[1] R.A. Borzooei, A.B. Saeid, A. Rezaei, A. Radfar and R. Ameri, On pseudo-BE-algebras, Discuss. Math. General Algebra and Appl. 33 (2013) 95-97. doi: 10.7151/dmgaa.1193

[2] M.A. Chaudhry, On BCH-algebras, Math. Japonica 36 (1991) 665-676.

[3] W.A. Dudek and Y.B. Jun, Pseudo-BCI-algebras, East Asian Math. J. 24 (2008) 187-190.

[4] G. Dymek, Atoms and ideals of pseudo-BCI-algebras, Comment. Math. 52 (2012) 73-90.

[5] G. Dymek, p-semisimple pseudo-BCI-algebras, J. Mult.-Valued Logic Soft Comput. 19 (2012) 461-474.

[6] G. Georgescu and A. Iorgulescu, Pseudo-MV algebras: a noncommutative extension of MV algebras, in: The Proc. of the Fourth International Symp. on Economic Informatics (Bucharest, Romania, May 1999) 961-968.

[7] G. Georgescu and A. Iorgulescu, Pseudo-BL algebras: a noncommutative extension of BL algebras, in: Abstracts of the Fifth International Conference FSTA 2000 (Slovakia, February, 2000) 90-92.

[8] G. Georgescu and A. Iorgulescu, Pseudo-BCK algebras: an extension of BCK algebras, in: Proc. of DMTCS'01: Combinatorics, Computability and Logic (Springer, London, 2001) 97-114.

[9] Q.P. Hu and X. Li, On BCH-algebras, Math. Seminar Notes 11 (1983) 313-320.

[10] Y. Imai and K. Iséki, On axiom systems of propositional calculi XIV, Proc. Japan Academy 42 (1966) 19-22.

[11] K. Iséki, An algebra related with a propositional culculus, Proc. Japan Academy 42 (1966) 26-29.

[12] Y.B. Jun, H.S. Kim and J. Neggers, On pseudo-BCI ideals of pseudo-BCI-algebras, Matem. Vesnik 58 (2006) 39-46.

[13] Y.B. Jun, H.S. Kim and J. Neggers, Pseudo-d-algebras, Information Sciences 179 (2009) 1751-1759. doi: 10.1016/j.ins.2009.01.021

[14] Y.H. Kim and K.S. So, On minimality in pseudo-BCI-algebras, Commun. Korean Math. Soc. 27 (2012) 7-13. doi: 10.4134/CKMS.2012.27.1.007

[15] K.J. Lee and Ch.H. Park, Some ideals of pseudo-BCI-algebras, J. Appl. Informatics 27 (2009) 217-231.

[16] J. Neggers and H.S. Kim, On d-algebras, Math. Slovaca 49 (1999) 19-26.

[17] A.B. Saeid and A. Namdar, On n-fold ideals in BCH-algebras and computation algorithms, World Applied Sciences Journal 7 (2009) 64-69.

[18] A. Wroński, BCK-algebras do not form a variety, Math. Japon. 28 (1983) 211-213.