Normal pseudo-BCK-algebras

• Autorzy: Dymek G.
• Języki publikacji: EN

Abstrakty

EN

A normal pseudo-BCK-algebra X is an algebra in which every subalgebra of X is an ideal of X. Characterizations of normal pseudo-BCK-algebras are given.

Słowa kluczowe

EN

pseudo-BCK-algebra; subalgebra; ideal; atom

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2011
• Tom: Vol. 51, [Z] 1
• Strony: 99--107
• 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] G. Dymek and A. Walendziak, Fuzzy ideals of pseudo-BCK algebras, Demonstr. Math., to appear.
• [2] 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.
• [3] G. Georgescu and A. Iorgulescu, Pseudo-BL algebras: a noncommutative extension of BLalgebras, Abstracts of The Fifth International Conference FSTA 2000, Slovakia, February 2000, 90-92.
• [4] G. Georgescu and A. Iorgulescu, Pseudo-MV algebras: a noncommutative extension of MValgebras, The Proceedings The Fourth International Symposium on Economic Informatics, INFOREC Printing House, Bucharest, Romania, May (1999), 961-968.
• [5] R. Halaš, J. Kühr, Deductive systems and annihilators of pseudo-BCK-algebras, Ital. J. Pure Appl. Math. 25 (2009).
• [6] W. Huang and Y. B. Jun, Ideals and subalgebras in BCI algebras, South. Asian Bull. Math. 26 (2002), 567-573.
• [7] Y. Imai, K. Iséki, On axiom systems of propositional calculi XIV, Proc. Japan Academy 42 (1966), 19-22.
• [8] A. Iorgulescu, Algebras of logic as BCK algebras, Editura ASE, Bucharest, 2008.
• [9] A. Iorgulescu, Classes of pseudo-BCK algebras, Part I, Journal of Multiplae-Valued Logic and Soft Computing 12 (2006), 71-130.
• [10] A. Iorgulescu, Classes of pseudo-BCK algebras, Part II, Journal of Multiplae-Valued Logic and Soft Computing 12 (2006), 575-629.
• [11] Y. B. Jun, Characterizations of pseudo-BCK algebras, Scientiae Mathematicae Japonicae 57 (2003), 265-270.
• [12] Y. B. Jun, H. S. Kim and J. Neggers, On pseudo-BCI ideals of pseudo BCI-algebras, Mat. Vesnik 58 (2006), 39-46.
• [13] J. Meng, S. M. Wei and Y. B. Jun, Normal BCI/BCK algebras, Comm. Korean Math. Soc. 9 (1994), 265-270.
• [14] A. Walendziak, On axiom systems of pseudo-BCK algebras, Bull. Malaysian Math. Sci. Soc. 34 (2011), 287-293.