Geodesic
Annihilators in BCK-algebras
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 1001-1007
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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 $\mathcal D (A)$.
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 $\mathcal D (A)$.
Classification : 03B60, 03G25, 06F35, 08A99
Keywords: BCK-algebra; deductive system; annihilator; pseudocomplement 
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     title = {Annihilators in {BCK-algebras}},
     journal = {Czechoslovak Mathematical Journal},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2003_53_4_a16/}
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Halaš, Radomír. Annihilators in BCK-algebras. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 1001-1007. http://geodesic.mathdoc.fr/item/CMJ_2003_53_4_a16/

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