| Title:
|
Implicative hyper $K$-algebras (English) |
| Author:
|
Zahedi, M. M. |
| Author:
|
Saeid, A. Borumand |
| Author:
|
Borzooei, R. A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
439-453 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we first define the notions of (weak, strong) implicative hyper $K$-algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper $K$-ideals. Also we obtain some relations between these notions and (weak) implicative hyper $K$-ideals. Finally, we study the implicative hyper $K$-algebras of order 3, in particular we obtain a relationship between the positive implicative hyper $K$-algebras and (weak, strong) implicative hyper $K$-algebras under a simple condition. (English) |
| Keyword:
|
hyper $K$-algebra |
| Keyword:
|
hyper $K$-ideal |
| Keyword:
|
(weak |
| Keyword:
|
strong) implicative hyper $K$-algebras |
| Keyword:
|
(weak) implicative hyper $K$-ideal |
| MSC:
|
03G25 |
| MSC:
|
06F35 |
| idZBL:
|
Zbl 1081.06030 |
| idMR:
|
MR2137150 |
| . |
| Date available:
|
2009-09-24T11:24:18Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127990 |
| . |
| Reference:
|
[1] A. Borumand Saeid, R. A. Borzooei and M. M. Zahedi: (Weak) implicative hyper $K$-ideals.Bull. Korean Math. Soc. 40 (2003), 123–137. MR 1958230, 10.4134/BKMS.2003.40.1.123 |
| Reference:
|
[2] R. A. Borzooei, P. Corsini and M. M. Zahedi: Some kinds of positive implicative hyper $K$-ideals.Journal of Discrete Mathematical Sciences and Cryptography 6 (2003), 97–108. MR 1988047, 10.1080/09720529.2003.10697966 |
| Reference:
|
[3] R. A. Borzooei, A. Hasankhani, M. M. Zahedi and Y. B. Jun: On hyper $K$-algebras.Math. Japon. 52 (2000), 113–121. MR 1783185 |
| Reference:
|
[4] R. A. Borzooei and M. M. Zahedi: Positive implicative hyper $K$-ideals.Scientiae Mathematicae Japonicae 53 (2001), 525–533. MR 1835922 |
| Reference:
|
[5] Y. Imai and K. Iseki: On axiom systems of propositional calculi.XIV Proc. Japan Academy 42 (1966), 19–22. MR 0195704 |
| Reference:
|
[6] Y. B. Jun, M. M. Zahedi, X. L. Xin and R. A. Borzooei: On hyper $BCK$-algebras.Ital. J. Pure Appl. Math. (2000), 127–136. MR 1793750 |
| Reference:
|
[7] F. Marty: Sur une generalization de la notion de groups.8th Congress Math. Scandinaves, Stockholm, 1934, pp. 45–49. |
| Reference:
|
[8] J. Meng and Y. B. Jun: $BCK$-Algebras.Kyung Moonsa, Seoul, 1994. MR 1297121 |
| Reference:
|
[9] D. Mundici: $MV$-algebras are categorically equivalent to bounded commutative $BCK$-algebras.Math. Japon. 31 (1986), 889–894. Zbl 0633.03066, MR 0870978 |
| Reference:
|
[10] M. M. Zahedi, R. A. Borzooei and H. Rezaei: Some classification of hyper $K$-algebras of order 3.Scientiae Mathematicae Japonicae 53 (2001), 133–142. MR 1821608 |
| Reference:
|
[11] M. M. Zahedi, R. A. Borzooei, Y. B. Jun and A. Hasankhani: Some results on hyper $K$-algebra.Scientiae Mathematicae 3 (2000), 53–59. MR 1758830 |
| . |
