| Title:
|
An ordered structure of pseudo-BCI-algebras (English) |
| Author:
|
Chajda, Ivan |
| Author:
|
Länger, Helmut |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
141 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
91-98 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In Chajda's paper (2014), to an arbitrary BCI-algebra the author assigned an ordered structure with one binary operation which possesses certain antitone mappings. In the present paper, we show that a similar construction can be done also for pseudo-BCI-algebras, but the resulting structure should have two binary operations and a set of couples of antitone mappings which are in a certain sense mutually inverse. The motivation for this approach is the well-known fact that every commutative BCK-algebra is in fact a join-semilattice and we try to obtain a similar result also for the non-commutative case and for pseudo-BCI-algebras which generalize BCK-algebras, see e.g. Imai and Iséki (1966) and Iséki (1966). (English) |
| Keyword:
|
pseudo-BCI-algebra |
| Keyword:
|
directoid |
| Keyword:
|
antitone mapping |
| Keyword:
|
pseudo-BCI-structure |
| MSC:
|
03G25 |
| MSC:
|
06F35 |
| idZBL:
|
Zbl 06562161 |
| idMR:
|
MR3475140 |
| DOI:
|
10.21136/MB.2016.7 |
| . |
| Date available:
|
2016-03-17T19:48:48Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144854 |
| . |
| Reference:
|
[1] Chajda, I.: A structure of BCI-algebras.Int. J. Theor. Phys. 53 (2014), 3391-3396. Zbl 1302.81032, MR 3253801, 10.1007/s10773-013-1739-4 |
| Reference:
|
[2] Chajda, I., Länger, H.: On the structure of pseudo-BCK algebras.(to appear) in J. Multiple-Valued Logic Soft Computing. |
| Reference:
|
[3] Chajda, I., L{ä}nger, H.: Directoids. An Algebraic Approach to Ordered Sets.Research and Exposition in Mathematics 32 Heldermann, Lemgo (2011). Zbl 1254.06002, MR 2850357 |
| Reference:
|
[4] Ciungu, L. C.: Non-commutative Multiple-Valued Logic Algebras.Springer Monographs in Mathematics Springer, Cham (2014). Zbl 1279.03003, MR 3112745 |
| Reference:
|
[5] Dudek, W. A., Jun, Y. B.: Pseudo-BCI algebras.East Asian Math. J. 24 (2008), 187-190. Zbl 1149.06010 |
| Reference:
|
[6] Dymek, G.: On two classes of pseudo-BCI-algebras.Discuss. Math., Gen. Algebra Appl. 31 (2011), 217-229. Zbl 1258.06014, MR 2953913, 10.7151/dmgaa.1184 |
| Reference:
|
[7] Dymek, G., Kozanecka-Dymek, A.: Pseudo-BCI-logic.Bull. Sect. Log., Univ. Łódź, Dep. Log. 42 (2013), 33-42. Zbl 1287.03058, MR 3077651 |
| Reference:
|
[8] Imai, Y., Iséki, K.: On axiom systems of propositional calculi. XIV.Proc. Japan Acad. 42 (1966), 19-22. Zbl 0156.24812, MR 0195704 |
| Reference:
|
[9] Is{é}ki, K.: An algebra related with a propositional calculus.Proc. Japan Acad. 42 (1966), 26-29. Zbl 0207.29304, MR 0202571 |
| . |
