| Title:
|
Operators on $GMV$-algebras (English) |
| Author:
|
Švrček, Filip |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
129 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
337-347 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Closure $GMV$-algebras are introduced as a commutative generalization of closure $MV$-algebras, which were studied as a natural generalization of topological Boolean algebras. (English) |
| Keyword:
|
$MV$-algebra |
| Keyword:
|
DRl-monoid |
| MSC:
|
06D35 |
| MSC:
|
06F05 |
| MSC:
|
06F99 |
| idZBL:
|
Zbl 1080.06502 |
| idMR:
|
MR2102608 |
| DOI:
|
10.21136/MB.2004.134044 |
| . |
| Date available:
|
2009-09-24T22:16:00Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134044 |
| . |
| Reference:
|
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| Reference:
|
[2] Chang, C. C.: A new proof of the completeness of the Łukasiewicz 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, 2000. MR 1786097 |
| Reference:
|
[4] Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures.Kluwer Acad. Publ., Dordrecht, 2000. MR 1861369 |
| Reference:
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[5] Georgescu, G., Iorgulescu, A.: Pseudo-$MV$-algebras.Multiple Valued Logic 6 (2001), 95–135. MR 1817439 |
| Reference:
|
[6] Kovář, T.: A General Theory of Dually Residuated Lattice Ordered Monoids.Ph.D. Thesis Palacký University, Olomouc, 1996. |
| Reference:
|
[7] Rachůnek, J.: DRl-semigroups and $MV$-algebras.Czechoslovak Math. J. 48 (1998), 365–372. MR 1624268, 10.1023/A:1022801907138 |
| Reference:
|
[8] Rachůnek, J.: $MV$-algebras are categorically equivalent to a class of DR$l_{1(i)}$-semigroups.Math. Bohem. 123 (1998), 437–441. MR 1667115 |
| Reference:
|
[9] Rachůnek, J.: A non-commutative generalization of $MV$-algebras.Czechoslovak Math. J. 52 (2002), 255–273. Zbl 1012.06012, MR 1905434, 10.1023/A:1021766309509 |
| Reference:
|
[10] Rachůnek, J.: Prime spectra of non-commutative generalizations of $MV$-algebras.Algebra Univers. 48 (2002), 151–169. Zbl 1058.06015, MR 1929902, 10.1007/PL00012447 |
| Reference:
|
[11] Rachůnek, J., Švrček, F.: $MV$-algebras with additive closure operators.Acta Univ. Palacki., Mathematica 39 (2000), 183–189. MR 1826361 |
| Reference:
|
[12] Rasiowa, H., Sikorski, R.: The Mathematics of Metamathematics.Panstw. Wyd. Nauk., Warszawa, 1963. MR 0163850 |
| Reference:
|
[13] Swamy, K. L. N.: Dually residuated lattice ordered semigroups.Math. Ann. 159 (1965), 105–114. Zbl 0138.02104, MR 0183797, 10.1007/BF01360284 |
| . |
