Czechoslovak Mathematical Journal, Vol. 53, No. 4, pp. 1001-1007, 2003

# Annihilators in BCK-algebras

Department of Algebra and Geometry, Palacky University, Tomkova 40, 779 00 Olomouc, Czech republic, e-mail: halas@aix.upol.cz

Abstract: We introduce the concepts of an annihilator and a relative annihilator of a given subset of a BCK-algebra $\Cal A$. We prove that annihilators of deductive systems of BCK-algebras are again deductive systems and moreover pseudocomplements in the lattice $\Cal D (A)$ of all deductive systems on $\Cal A$. Moreover, relative annihilators of $C\in\Cal D (A)$ with respect to $B \in\Cal D (A)$ are introduced and serve as relative pseudocomplements of $C$ w.r.t. $B$ in $\Cal D (A)$.

Keywords: BCK-algebra, deductive system, annihilator, pseudocomplement

Classification (MSC 2000): 08A99, 03B60

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