| Title:
|
Deductive systems of BCK-algebras (English) |
| Author:
|
Celani, Sergio A. |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
27-32 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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]. (English) |
| Keyword:
|
BCK-algebras |
| Keyword:
|
deductive system |
| Keyword:
|
irreducible deductive system |
| Keyword:
|
Heyting algebras |
| Keyword:
|
annihilators |
| MSC:
|
03F35 |
| MSC:
|
03G25 |
| MSC:
|
06D20 |
| MSC:
|
06F35 |
| idZBL:
|
Zbl 1069.06010 |
| idMR:
|
MR2124600 |
| . |
| Date available:
|
2009-08-21T12:53:50Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132945 |
| . |
| Reference:
|
[1] Celani S.: A note on Homomorphisms of Hilbert Algebras.International Journal of Mathematics and Mathematical Science 29, 1 (2002), 55–61. Zbl 0993.03089, MR 1892332 |
| Reference:
|
[2] Chajda I., Halaš R., Zedník J.: Filters and Annihilators in Implication Algebras.Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 37 (1998), 41–45. Zbl 0967.03059, MR 1690472 |
| Reference:
|
[3] Chajda I., Halaš R., Jun J. B. : Annihilators and deductive systems in commutative Hilbert algebras.Comment. Math. Univ. Carolinae 43, 3 (2002) 407–417. Zbl 1070.03043, MR 1920517 |
| Reference:
|
[4] Jun Y. B., Roh E. H., Meng J.: Annihilators in BCI-algebras.Math. Japonica 43, 3 (1996), 559–562. Zbl 0854.06028, MR 1391864 |
| Reference:
|
[5] Halaš R.: Annihilators of BCK-algebras.Czech. Math. Journal 53, 128 (2003), 1001–1007. MR 2018845 |
| Reference:
|
[6] Halaš R.: Remarks on commutative Hilbert algebras.Math. Bohemica 127, 4 (2002), 525–529. Zbl 1008.03039, MR 1942638 |
| Reference:
|
[7] Kondo M.: Annihilators in BCK-algebras.Math. Japonica 49, 3 (1999), 407–410. Zbl 0932.06014, MR 1697812 |
| Reference:
|
[8] Pałasiński M.: Ideals in BCK-algebras which are lower semilattices.Math. Japonica 26, 2 (1981), 245–250. Zbl 0464.03056, MR 0620466 |
| Reference:
|
[9] Pałasiński M.: On ideal and congruence lattices of BCK-algebras.Math. Japonica 26, 5 (1981), 543–544. Zbl 0476.03064, MR 0636589 |
| Reference:
|
[10] Wei S. M., Jun Y. B.: Ideal lattices of BCI-algebras.Math. Japonica 44, 2 (1996), 303–305. Zbl 0878.06011, MR 1416268 |
| . |
