Some properties of pseudo-BCI algebras

• Autorzy: Dymek G.

Identyfikatory

DOI

10.14708/cm.v58i1-2.6388

• Języki publikacji: EN

Abstrakty

EN

In this paper the notion of an essential closed deductive system of a pseudo-BCI algebra is defined and investigated. Among other things, it is proved that such a deductive system contains all coatoms of the pseudo-BCI algebra. Also, the notions of homomorphisms and semihomomorphisms of pseudo-BCI algebras are studied and some of their properties are presented.

Słowa kluczowe

EN

pseudo-BCI algebra; deductive system; homomorphism

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2018
• Tom: Vol. 58, No. 1/2
• Strony: 19--35
• Opis fizyczny: Bibliogr. 13 poz., rys., tab.

Twórcy

autor

Dymek G.

• Institute of Mathematics and Computer Science, 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, Atoms and ideals of pseudo-BCI-algebras, Comment. Math. 52 (2012), 73-90, DOI 10.14708/cm.v52i1.5328.
• [3] G. Dymek, Deductive systems and ideals of pseudo-BCI-algebras, Recent Developments in Mathematics and Informatics (A. Zapała, ed.), Contemporary Mathematics and Computer Science, vol. 1, Wydawnictwo KUL, Lublin, 2016, 37-48.
• [4] G. Dymek, On compatible deductive systems of pseudo-BCI-algebras, J. Mult.-Valued Logic Soft Comput. 22 (2014), 167-187.
• [5] G. Dymek, On irreducible and prime deductive systems of pseudo-BCI-algebras, Comment. Math. 54 (2014), 67-78, DOI 10.14708/cm.v54i1.763.
• [6] G. Dymek, On pseudo-BCI-algebras, Ann. Univ. Mariae Curie-Skłodowska Sect. A 69 (2015), 59-71, DOI 10.1515/umcsmath-2015-0012.
• [7] G. Dymek, p-semisimple pseudo-BCI-algebras, J. Mult.-Valued Logic Soft Comput. 19 (2012), 461-474.
• [8] G. Dymek, Various deductive systems of pseudo-BCI algebras, J. Mult.-Valued Logic Soft Comput. 28 (2017), 619-641.
• [9] 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.
• [10] 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.
• [11] G. Georgescu and A. Iorgulescu, Pseudo-MV algebras: a noncommutative extension of MV-algebras, (Bucharest, May (1999)), The Proceedings The Fourth International Symposium on Economic Informatics, INFOREC Printing House, Bucharest, 961-968.
• [12] Y. Imai and K. Iséki, On axiom systems of propositional calculi XIV, Proc. Japan Acad. 42 (1966), 19-22, DOI 10.3792/pja/1195522169.
• [13] K. Iséki, An algebra related with a propositional calculus, Proc. Japan Acad. 42 (1966), 26-29, DOI 10.3792/pja/1195522171.