Annihilators in BCK-algebras

Radomír Halaš

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 4, page 1001-1007
  • ISSN: 0011-4642

Abstract

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

How to cite

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Halaš, Radomír. "Annihilators in BCK-algebras." Czechoslovak Mathematical Journal 53.4 (2003): 1001-1007. <http://eudml.org/doc/30830>.

@article{Halaš2003,
abstract = {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 $\mathcal \{D\} (A)$.},
author = {Halaš, Radomír},
journal = {Czechoslovak Mathematical Journal},
keywords = {BCK-algebra; deductive system; annihilator; pseudocomplement; BCK-algebra; deductive system; annihilator; pseudocomplement},
language = {eng},
number = {4},
pages = {1001-1007},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Annihilators in BCK-algebras},
url = {http://eudml.org/doc/30830},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Halaš, Radomír
TI - Annihilators in BCK-algebras
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 4
SP - 1001
EP - 1007
AB - 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 $\mathcal {D} (A)$.
LA - eng
KW - BCK-algebra; deductive system; annihilator; pseudocomplement; BCK-algebra; deductive system; annihilator; pseudocomplement
UR - http://eudml.org/doc/30830
ER -

References

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  2. Algebraizable Logics, Memoirs of the American Math. Soc., No 396, Providence, Rhode Island, 1989. (1989) MR0973361
  3. The lattice of deductive systems on Hilbert algebras, Southeast Asian Bull. Math., to appear. (to appear) Zbl1010.03054MR2046584
  4. Stabilizers in Hilbert algebras, Multiple Valued Logic 8 (2002), 139–148. (2002) MR1957649
  5. Sur les algébres de Hilbert, Collection de Logique Math. Ser. A (Ed. Hermann) 21 (1967), 177–198. (1967) 
  6. On ideals and congruences in BCC-algebras, Czechoslovak Math. J (to appear). (to appear) Zbl0927.06013MR1614060
  7. An introduction to the theory of BCK-algebras, Math. Japon. 23 (1978), 1–26. (1978) MR0500283
  8. Ideal theory of BCK-algebras, Math. Japon. 21 (1976), 351–366. (1976) MR0441816
  9. Investigations into implicational S5, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 10 (1964), 203–220. (1964) MR0163843

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