Deductive systems of BCK-algebras

Sergio A. Celani

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2004)

  • Volume: 43, Issue: 1, page 27-32
  • ISSN: 0231-9721

Abstract

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In this paper we shall give some results on irreducible deductive systems in BCK-algebras and we shall prove that the set of all deductive systems of a BCK-algebra is a Heyting algebra. As a consequence of this result we shall show that the annihilator F * of a deductive system F is the the pseudocomplement of F . These results are more general than that the similar results given by M. Kondo in [7].

How to cite

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Celani, Sergio A.. "Deductive systems of BCK-algebras." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 43.1 (2004): 27-32. <http://eudml.org/doc/32355>.

@article{Celani2004,
abstract = {In this paper we shall give some results on irreducible deductive systems in BCK-algebras and we shall prove that the set of all deductive systems of a BCK-algebra is a Heyting algebra. As a consequence of this result we shall show that the annihilator $F^\{\ast \}$ of a deductive system $F$ is the the pseudocomplement of $F$. These results are more general than that the similar results given by M. Kondo in [7].},
author = {Celani, Sergio A.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {BCK-algebras; deductive system; irreducible deductive system; Heyting algebras; annihilators; deductive systems; BCK-algebras; Heyting algebra; annihilator; pseudo-complement},
language = {eng},
number = {1},
pages = {27-32},
publisher = {Palacký University Olomouc},
title = {Deductive systems of BCK-algebras},
url = {http://eudml.org/doc/32355},
volume = {43},
year = {2004},
}

TY - JOUR
AU - Celani, Sergio A.
TI - Deductive systems of BCK-algebras
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2004
PB - Palacký University Olomouc
VL - 43
IS - 1
SP - 27
EP - 32
AB - In this paper we shall give some results on irreducible deductive systems in BCK-algebras and we shall prove that the set of all deductive systems of a BCK-algebra is a Heyting algebra. As a consequence of this result we shall show that the annihilator $F^{\ast }$ of a deductive system $F$ is the the pseudocomplement of $F$. These results are more general than that the similar results given by M. Kondo in [7].
LA - eng
KW - BCK-algebras; deductive system; irreducible deductive system; Heyting algebras; annihilators; deductive systems; BCK-algebras; Heyting algebra; annihilator; pseudo-complement
UR - http://eudml.org/doc/32355
ER -

References

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  7. Kondo M., Annihilators in BCK-algebras, Math. Japonica 49, 3 (1999), 407–410. (1999) Zbl0932.06014MR1697812
  8. Pałasiński M., Ideals in BCK-algebras which are lower semilattices, Math. Japonica 26, 2 (1981), 245–250. (1981) Zbl0464.03056MR0620466
  9. Pałasiński M., On ideal and congruence lattices of BCK-algebras, Math. Japonica 26, 5 (1981), 543–544. (1981) Zbl0476.03064MR0636589
  10. Wei S. M., Jun Y. B., Ideal lattices of BCI-algebras, Math. Japonica 44, 2 (1996), 303–305. (1996) Zbl0878.06011MR1416268

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