Atoms and ideals of pseudo-BCI-algebras

• Autorzy: Dymek G.
• Języki publikacji: EN

Abstrakty

EN

The main subject of the paper are atoms and ideals of a pseudo-BCI-algebra. Many different characterizations of them are given. Some connections between ideals and subalgebras are presented. Conditions for the set At(X) of atoms of a pseudo-BCI-algebra X to be an ideal of X are established.

Słowa kluczowe

EN

pseudo-BCI-algebra; atom; closed ideals

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2012
• Tom: Vol. 52, [Z] 1
• Strony: 73--90
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Dymek G.

• Faculty of Mathematics and Natural Sciences, The John Paul Ii Catholic University of Lublin Konstantynów 1H, 20-708 Lublin, Poland,

Bibliografia

• [1] W.A. Dudek and Y.B. Jun, Pseudo-BCI algebras, East Asian Math. J. 24 (2008), 187-190.
• [2] G. Dymek, p-semisimple pseudo-BCI algebras, J. Mult.-Valued Logic Soft Comput., to appear.
• [3] G. Georgescu and A. Iorgulescu, Pseudo-BCK algebras: an extension of BCK-algebras, Proceedings of DMTCS'01: Combinatorics, Computability and Logic, Springer, London, 2001, 97-114.
• [4] G. Georgescu and A. Iorgulescu, Pseudo-BL algebras: a noncommutative extension of BL-algebras, Abstracts of The Fifth International Conference FSTA 2000, Slovakia, February 2000, 90-92.
• [5] G. Georgescu and A. Iorgulescu, Pseudo-MV algebras: a noncommutative extension of MV-algebras, The Proceedings The Fourth International Symposium on Economic Informatics, INFOREC Printing House, Bucharest, Romania, May (1999), 961-968.
• [6] C.S. Hoo, Filters and ideals in BCI-algebras, Math. Japon. 36 (1991), 987-997.
• [7] W. Huang and Y.B. Jun, Ideals and subalgebras in BCI-algebras, Southeast Asian Bull. Math. 26 (2002), 567-573.
• [8] A. Iorgulescu, Algebras of logic as BCK algebras, Editura ASE, Bucharest, 2008.
• [9] K. Iseki, An algebra related with a propositional calculus, Proc. Japan Acad. 42 (1966), 26-29.
• [10] K. Iseki, On BCI-algebras, Math. Seminar Notes 8 (1980), 125-130.
• [11] Y.B. Jun, H.S. Kim and J. Neggers, On pseudo-BCI ideals of pseudo BCI-algebras, Mat. Vesnik 58 (2006), 39-46.
• [12] Y.B. Jun, X.L. Xin and E.H. Roh, The role of atoms in BCI-algebras, Soochow J. Math. 30 (2004), 491-506.
• [13] K.J. Lee and C.H. Park, Some ideals of pseudo-BCI algebras, J. Appl. Math. Informatics 27 (2009), 217-231
• [14] J. Meng and X.L. Xin, Characterizations of atoms in BCI-algebras, Math. Japon. 37 (1992), 359-361.