Geodesic
On ideals of pseudo-BCH-algebras
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 70 (2016) no. 1.

Voir la notice de l'article provenant de la source Library of Science

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 
@article{AUM_2016_70_1_a4,
     author = {Walendziak, Andrzej},
     title = {On ideals of {pseudo-BCH-algebras}},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica },
     publisher = {mathdoc},
     volume = {70},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2016_70_1_a4/}
}
TY  - JOUR
AU  - Walendziak, Andrzej
TI  - On ideals of pseudo-BCH-algebras
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
PY  - 2016
VL  - 70
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2016_70_1_a4/
LA  - en
ID  - AUM_2016_70_1_a4
ER  - 
%0 Journal Article
%A Walendziak, Andrzej
%T On ideals of pseudo-BCH-algebras
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
%D 2016
%V 70
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2016_70_1_a4/
%G en
%F AUM_2016_70_1_a4
Walendziak, Andrzej. On ideals of pseudo-BCH-algebras. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 70 (2016) no. 1. http://geodesic.mathdoc.fr/item/AUM_2016_70_1_a4/

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

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

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

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

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

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

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

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

[9] 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.

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

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

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

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

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

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

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

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

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

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