| Title:
|
Additive closure operators on abelian unital $l$-groups (English) |
| Author:
|
Švrček, Filip |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
153-158 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper an additive closure operator on an abelian unital $l$-group $(G,u)$ is introduced and one studies the mutual relation of such operators and of additive closure ones on the $MV$-algebra $\Gamma (G,u)$. (English) |
| Keyword:
|
$MV$-algebra |
| Keyword:
|
$l$-group. |
| MSC:
|
06D35 |
| MSC:
|
06F20 |
| idZBL:
|
Zbl 1125.06014 |
| idMR:
|
MR2321307 |
| . |
| Date available:
|
2009-08-21T07:04:41Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133443 |
| . |
| Reference:
|
[1] Chang C. C.: Algebraic analysis of many valued logics.Trans. Amer. Math. Soc. 88 (1958), 467–490. Zbl 0084.00704, MR 0094302 |
| Reference:
|
[2] Chang C. C.: A new proof of the completeness of the Lukasiewicz axioms.Trans. Amer. Math. Soc. 93 (1959), 74–80. Zbl 0093.01104, MR 0122718 |
| Reference:
|
[3] Cignoli R. O. L., D’Ottaviano I. M. L., Mundici D.: Algebraic Foundations of Many-valued Reasoning. : Kluwer Acad. Publ., Dordrecht–Boston–London.2000. MR 1786097 |
| Reference:
|
[4] Dvurečenskij A., Pulmannová S.: New Trends in Quantum Structures. : Kluwer Acad. Publ., Dordrecht.2000. MR 1861369 |
| Reference:
|
[5] Mundici D.: Interpretation of AF $C^{*}\! $-algebras in Lukasiewicz sentential calculus.J. Funct. Analys. 65 (1986), 15–63. Zbl 0597.46059, MR 0819173 |
| Reference:
|
[6] Rachůnek J., Švrček F.: MV-algebras with additive closure operators.Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 39 (2000), 183–189. Zbl 1039.06005, MR 1826361 |
| . |
