Previous |  Up |  Next


Title: Annihilators in BCK-algebras (English)
Author: Halaš, Radomír
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 53
Issue: 4
Year: 2003
Pages: 1001-1007
Summary lang: English
Category: math
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 $\mathcal D (A)$. (English)
Keyword: BCK-algebra
Keyword: deductive system
Keyword: annihilator
Keyword: pseudocomplement
MSC: 03B60
MSC: 03G25
MSC: 06F35
MSC: 08A99
idZBL: Zbl 1080.06035
idMR: MR2018845
Date available: 2009-09-24T11:08:33Z
Last updated: 2020-07-03
Stable URL:
Reference: [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
Reference: [2] W. J. Blok and D. Pigozzi: Algebraizable Logics.Memoirs of the American Math. Soc., No 396, Providence, Rhode Island, 1989. MR 0973361
Reference: [3] I. Chajda: The lattice of deductive systems on Hilbert algebras.Southeast Asian Bull. Math., to appear. Zbl 1010.03054, MR 2046584
Reference: [4] I. Chajda and R. Halaš: Stabilizers in Hilbert algebras.Multiple Valued Logic 8 (2002), 139–148. MR 1957649
Reference: [5] A. Diego: Sur les algébres de Hilbert.Collection de Logique Math. Ser. A (Ed. Hermann) 21 (1967), 177–198.
Reference: [6] W. A. Dudek: On ideals and congruences in BCC-algebras.Czechoslovak Math. J (to appear). Zbl 0927.06013, MR 1614060
Reference: [7] K. Iséki and S. Tanaka: An introduction to the theory of BCK-algebras.Math. Japon. 23 (1978), 1–26. MR 0500283
Reference: [8] K. Iséki and S. Tanaka: Ideal theory of BCK-algebras.Math. Japon. 21 (1976), 351–366. MR 0441816
Reference: [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


Files Size Format View
CzechMathJ_53-2003-4_17.pdf 305.3Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo