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Keywords:
BCK-algebra; deductive system; annihilator; pseudocomplement
BCK-algebra; deductive system; annihilator; pseudocomplement
Summary:
We introduce the concepts of an annihilator and a relative annihilator of a given subset of a BCK-algebra $\mathcal A$. We prove that annihilators of deductive systems of BCK-algebras are again deductive systems and moreover pseudocomplements in the lattice $\mathcal D (A)$ of all deductive systems on $\mathcal A$. Moreover, relative annihilators of $C\in \mathcal D (A)$ with respect to $B \in \mathcal D (A)$ are introduced and serve as relative pseudocomplements of $C$ w.r.t. $B$ in $\mathcal D (A)$.
References:
[1] H. A. S. Abujabal, M. A. Obaid and M. Aslam: On annihilators of BCK-algebras. Czechoslovak Math. J. 45(120) (1995), 727–735. MR 1354929
[2] W. J. Blok and D. Pigozzi: Algebraizable Logics. Memoirs of the American Math. Soc., No 396, Providence, Rhode Island, 1989. MR 0973361
[3] I. Chajda: The lattice of deductive systems on Hilbert algebras. Southeast Asian Bull. Math., to appear. MR 2046584 | Zbl 1010.03054
[4] I. Chajda and R. Halaš: Stabilizers in Hilbert algebras. Multiple Valued Logic 8 (2002), 139–148. MR 1957649
[5] A. Diego: Sur les algébres de Hilbert. Collection de Logique Math. Ser. A (Ed. Hermann) 21 (1967), 177–198.
[6] W. A. Dudek: On ideals and congruences in BCC-algebras. Czechoslovak Math. J (to appear). MR 1614060 | Zbl 0927.06013
[7] K. Iséki and S. Tanaka: An introduction to the theory of BCK-algebras. Math. Japon. 23 (1978), 1–26. MR 0500283
[8] K. Iséki and S. Tanaka: Ideal theory of BCK-algebras. Math. Japon. 21 (1976), 351–366. MR 0441816
[9] C. A. Meredith and A. N. Prior: Investigations into implicational S5. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 10 (1964), 203–220. MR 0163843
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