A NOTE ON IDEALS AND FILTERS IN BCC-ALGEBRA

Year 2018, Volume: 1 Issue: 2, 190 - 194, 31.07.2018

Daniel A. Romano

Abstract

In this article we introduce and analyze a new concept of BCC-filters in BCC-algebra. In addition, the relationship of this new concept with BCC-ideals has been analyzed also.

Keywords

BCC-algebra, BCC-ideal

References

• S. A. Celani. Deductive systems of BCK-algebras. \emph{Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica}, \textbf{43}(2004), 27-–32.
• W. A. Dudek. On BCC-algebras. \emph{Logique and Analyse}, \textbf{129-130} (1990), 103--111.
• W. A. Dudek. On proper BCC-algebras. \emph{Bull. Inst. Math. Academia Sinica}, \textbf{20}(1992), 137-150.
• W. A. Dudek and X. H. Zhang. On ideals and congruences in BCC-algebras. \emph{Czechoslovak Math. J.}, \textbf{48}(1)(1998), 21-–29.
• W. A. Dudek. A new characterization of ideals in BCC-algebras. \emph{Novi Sad J. Math.}, 29(1)(1999), 139--145.
• W. A. Dudek and X. H. Zhang. Initial segemnts in BCC-algebras. \emph{Mathematica Moravica}, \textbf{4}(2000), 27--34.
• R. Hala\v s. Annihilators in BCK-algebras. \emph{Czechoslovak Math. J.}, \textbf{53}(4)(2003), 1001--1007.
• B. Karamdin and S. A. Bhatti. Ideals and branches of BCC-algebras. \emph{East Asian Math. J.}, \textbf{23} (2007), 247--255.
• Y. Komori. The variety generated by BCC-algebras is finitely based. \emph{Reports Fac. Sci. Shizuoka Univ.}, \textbf{17}(1983), 13--16.
• Y. Komori. The class of BCC-algebras is not a variety. \emph{Math. Japonica}, \textbf{29} (1984), 391--394.