Geodesic
On branchwise commutative pseudo-BCH algebras
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 2.

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Basic properties of branches of pseudo-BCH algebras are described. Next, the concept of a branchwise commutative pseudo-BCH algebra is introduced. Some conditions equivalent to branchwise commutativity are given. It is proved that every branchwise commutative pseudo-BCH algebra is a pseudo-BCI algebra.
Keywords: (Pseudo-)BCK/BCI/BCH-algebra, atom, branch, branchwise commutativity 
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Walendziak, Andrzej. On branchwise commutative pseudo-BCH algebras. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 2. http://geodesic.mathdoc.fr/item/AUM_2017_71_2_a3/

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

[2] Dudek, W. A., Zhang, X., Wang, Y., Ideals and atoms of BZ-algebras, Math. Slovaca 59 (2009), 387-404.

[3] Dudek, W. A., Karamdin, B., Bhatti, S. A., Branches and ideals of weak BCCalgebras, Algebra Colloquium 18 (Special) (2011), 899-914.

[4] Dymek, G., On two classes of pseudo-BCI-algebras, Discuss. Math. Gen. Algebra Appl. 31 (2011), 217-230.

[5] Georgescu, G., Iorgulescu, A., 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.

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

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

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

[9] Imai, Y., Iseki, K., On axiom systems of propositional calculi XIV, Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 19-22.

[10] Iorgulescu A., Algebras of Logic as BCK-Algebras, Bucharest 2008.

[11] Iorgulescu, A., New generalizations of BCI, BCK and Hilbert algebras - Part I, J. Mult.-Valued Logic Soft Comput. 27 (2016), 353-406.

[12] Iorgulescu, A., New generalizations of BCI, BCK and Hilbert algebras - Part II, J. Mult.-Valued Logic Soft Comput. 27 (2016), 407-456.

[13] Iseki, K., An algebra related with a propositional calculus, Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 26-29.

[14] Walendziak, A., Pseudo-BCH-algebras, Discuss. Math. Gen. Algebra Appl. 35 (2015), 1-15.

[15] Walendziak, A., On ideals of pseudo-BCH-algebras, Ann. Univ. Mariae Curie-Skłodowska Sect. A 70 (2016), 81-91.

[16] Walendziak, A., Strong ideals and horizontal ideals in pseudo-BCH-algebras, Ann. Univ. Paedagog. Crac. Stud. Math. 15 (2016), 15-25.

[17] Zhang, X., Ye, R., BZ-algebra and group, J. of Mathematical and Physical Sciences 29 (1995), 223-233.

[18] Zhang, X., Wang, Y., Dudek, W. A., T-ideals in BZ-algebras and T-type BZ-algebras, Indian J. Pure Appl. Math. 34 (2003), 1559-1570.