On ideals of pseudo-BCH-algebras

Andrzej Walendziak

Abstract


In this paper we introduce the notion of a disjoint union of pseudo-BCH-algebras and describe ideals in such algebras. We also investigate ideals of direct products of pseudo-BCH-algebras. Moreover, we establish conditions for the set of all minimal elements of a pseudo-BCH-algebra X to be an ideal of X.

Keywords


(Pseudo-)BCK/BCI/BCH-algebra; disjoint union; ideal; centre

Full Text:

PDF

References


Dudek, W. A., Thomys, J., On decompositions of BCH-algebras, Math. Japon. 35 (1990), 1131-1138.

Dudek, W. A., Zhang, X., On atoms in BCC-algebras, Discuss. Math. Algebra Stochastic Methods 15 (1995), 81-85.

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

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

Dudek, W. A., Karamdin, B., Bhatti, S. A., Branches and ideals of weak BCC-algebras, Algebra Colloq. 18 (Special) (2011), 899-914.

Dvurecenskij, A., Pulmannova, S., New Trends in Quantum Structures, Kluwer Acad. Publ., Dordrecht; Ister Science, Bratislava, 2000.

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

Dymek, G., On pseudo-BCI-algebras, Ann. Univ. Mariae Curie-Skłodowska Sect. A 69 (1) (2015), 59-71.

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

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

Imai, Y., Iseki, K., On axiom systems of propositional calculi XIV, Proc. Japan Acad. 42 (1966), 19-22.

Iseki, K., An algebra related with a propositional culculus, Proc. Japan Acad. 42 (1966), 26-29.

Iorgulescu, A., Algebras of Logic as BCK-algebras, Editura ASE, Bucharest, 2008.

Kim, K. H., Roh, E. H., The role of (A^+) and (A(X)) in BCH-algebras, Math. Japon. 52 (2000), 317-321.

Kim, Y. H., So, K. S., On minimality in pseudo-BCI-algebras, Commun. Korean Math. Soc. 27 (2012), 7-13.

Lee, K. J, Park, C. H., Some ideals of pseudo-BCI-algebras, J. Appl. Math. Inform. 27 (2009), 217-231.

Meng, J., Xin, X. L., Characterizations of atoms in BCI-algebras, Math. Japon. 37 (1992), 359-361.

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

Walendziak, A., Wojciechowska-Rysiawa, M., Fuzzy ideals of pseudo-BCH-algebras, Mathematica Aeterna 5 (2015), 867-881.




DOI: http://dx.doi.org/10.17951/a.2016.70.1.81
Date of publication: 2016-07-04 15:44:01
Date of submission: 2016-07-01 21:12:29


Statistics


Total abstract view - 1216
Downloads (from 2020-06-17) - PDF - 599

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2016 Andrzej Walendziak