Strong ideals and horizontal ideals in pseudo-BCH-algebras

Andrzej Walendziak


In this paper we define strong ideals and horizontal ideals in pseudo-BCH-algebras and investigate the properties and characterizations of them.


(Pseudo-)BCK/BCI/BCH-algebra, closed ideal, strong ideal, horizontal ideal, centre

Mathematics Subject Classification (2010)

03G25; 06F35


Bhatti, Shaban, and Xiao Hong Zhang. "Strong ideals, associative ideals and p-ideals in BCI-algebras." Punjab Univ. J. Math. (Lahore) 27 (1994): 113-120.

Dudek, Wiesław A., and Young-Bae Jun. "Pseudo-BCI-algebras." East Asian Math. J. 24, no. 2 (2008): 187-190.

Dymek, Grzegorz. "On two classes of pseudo-BCI-algebras." Discuss. Math. Gen. Algebra Appl. 31, no. 2 (2011): 217-230.

Dymek, Grzegorz. "Atoms and ideals of pseudo-BCI-algebras." Comment. Math. 52, no. 1 (2012): 73-90.

Dymek, Grzegorz. "p-semisimple pseudo-BCI-algebras." J. Mult.-Valued Logic Soft Comput. 19, no. 5-6 (2012): 461-474.

Dymek, Grzegorz. "On the category of pseudo-BCI-algebras." Demonstratio Math. 46, no. 4 (2013): 631-644.

Dymek, Grzegorz. "On pseudo-BCI-algebras." Ann. Univ. Mariae Curie-Skłodowska Sect. A 69, no. 1 (2015): 59-71.

Georgescu, George, and Afrodita Iorgulescu. "Pseudo-MV algebras: a noncommutative extension of MV algebras." In Information technology (Bucharest, 1999), 961-968. Bucharest: Inforec, 1999.

Georgescu, George, and Afrodita Iorgulescu. "Pseudo-BL algebras: anoncommutative extension of BL algebras." In Abstracts of the Fifth International Conference FSTA 2000, Liptovský Ján, The Slovak Republic. January 31 - February 4, 2000, 90-92.

Georgescu, George, and Afrodita Iorgulescu. "Pseudo-BCK algebras: an extension of BCK algebras." In Combinatorics, computability and logic: Proceedings of the Third International Conference on Combinatorics, Computability and Logic , edited by C.S Calude et al. Discrete Math. Theor. Comput. Sci., 97-114. London: Springer, 2001.

Hu, Qing Ping, and Xin Li. "On BCH-algebras." Math. Sem. Notes Kobe Univ. 11, no. 2 (1983): 313-320.

Huang Yisheng. BCI-algebra. Beijing: Science Press, 2006.

Imai, Yasuyuki, and Kiyoshi Iseki. "On axiom systems of propositional calculi. XIV." Proc. Japan Acad. 42 (1966): 19-22.

Iseki, Kiyoshi. "An algebra related with a propositional calculus." Proc. Japan Acad. 42 (1966): 26-29.

Jun, Young Bae, Hee Sik Kim, and Joseph Neggers. "On pseudo-BCI ideals of pseudo-BCI algebras." Mat. Vesnik 58, no. 1-2 (2006): 39-46.

Kim, Kyung Ho, and Eun Hwan Roh. "The role of A+ and A(X) in BCH-algebras." Math. Japon. 52, no. 2 (2000): 317-321.

Kim, Young Hee, and Keum Sook So. "On minimality in pseudo-BCI-algebras." Commun. Korean Math. Soc. 27, no. 1 (2012): 7-13.

Lee, Kyoung Ja, and Chul Hwan Park. "Some ideals of pseudo-BCI-algebras." J. Appl. Math. & Informatics 27 (2009): 217-231.

Lu Yin-Feng, and Xiao-Hong Zhang, "Q-type pseudo-BCI algebras and 2-type pseudo-q filters." Journal of Ningbo University 24, no. 2 (2011): 56-60.

Walendziak, Andrzej. "Pseudo-BCH-algebras." Discuss. Math. Gen. Algebra Appl. 35, no. 1 (2015): 5-19.

Walendziak, Andrzej. "On ideals of pseudo-BCH-algebras." Ann. Univ. Mariae Curie-Skłodowska, Sect. A (in press).

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