| Title:
|
A non-commutative generalization of $MV$-algebras (English) |
| Author:
|
Rachůnek, Jiří |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
255-273 |
| . |
| Category:
|
math |
| . |
| MSC:
|
06D35 |
| MSC:
|
06F05 |
| MSC:
|
06F15 |
| idZBL:
|
Zbl 1012.06012 |
| idMR:
|
MR1905434 |
| . |
| Date available:
|
2009-09-24T10:50:41Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127715 |
| . |
| Reference:
|
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| Reference:
|
[2] A. Bigard, K. Keimel and S. Wolfenstein: Groupes et Anneaux Réticulés.SpringerVerlag, Berlin-Heidelberg-New York, 1977. MR 0552653 |
| Reference:
|
[3] S. Burris and H. P. Sankappanavar: A Course in Universal Algebra.Springer-Verlag, Berlin-Heidelberg-New York, 1981. MR 0648287 |
| Reference:
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[4] C. C. Chang: Algebraic analysis of many valued logics.Trans. Amer. Math. Soc. 88 (1958), 467–490. Zbl 0084.00704, MR 0094302, 10.1090/S0002-9947-1958-0094302-9 |
| Reference:
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[5] C. C. Chang: A new proof of the completeness of the Lukasiewicz axioms.Trans. Amer. Math. Soc. 93 (1959), 74–80. Zbl 0093.01104, MR 0122718 |
| Reference:
|
[6] R. Cignoli: Free lattice-ordered abelian groups and varieties of $MV$-algebras.Proc. IX. Latin. Amer. Symp. Math. Log., Part 1, Not. Log. Mat. 38 (1993), 113–118. Zbl 0827.06012, MR 1332526 |
| Reference:
|
[7] : Lattice-Ordered Groups (Advances and Techniques).A. M. W. Glass and W. Charles Holland (eds.), Kluwer Acad. Publ., Dordrecht-Boston-London, 1989. Zbl 0705.06001, MR 1036072 |
| Reference:
|
[8] C. S. Hoo: $MV$-algebras, ideals and semisimplicity.Math. Japon. 34 (1989), 563–583. Zbl 0677.03041, MR 1005257 |
| Reference:
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[9] V. M. Kopytov and N. Ya. Medvedev: The Theory of Lattice Ordered Groups.Kluwer Acad. Publ., Dordrecht-Boston-London, 1994. MR 1369091 |
| Reference:
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[10] T. Kovář: A general theory of dually residuated lattice ordered monoids.Thesis, Palacký University Olomouc, 1996. |
| Reference:
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[11] D. Mundici: Interpretation of $AF C^{*}$-algebras in Łukasiewicz sentential calculus.J. Funct. Anal. 65 (1986), 15–63. Zbl 0597.46059, MR 0819173 |
| Reference:
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[12] D. Mundici: $MV$-algebras are categorically equivalent to bounded commutative $BCK$-algebras.Math. Japon. 31 (1986), 889–894. Zbl 0633.03066, MR 0870978 |
| Reference:
|
[13] J. Rachůnek: $DRl$-semigroups and $MV$-algebras.Czechoslovak Math. J. 48(123) (1998), 365–372. MR 1624268, 10.1023/A:1022801907138 |
| Reference:
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[14] J. Rachůnek: $MV$-algebras are categorically equivalent to a class of $DRl_{1(i)}$-semigroups.Math. Bohem. 123 (1998), 437–441. MR 1667115 |
| Reference:
|
[15] K. L. N. Swamy: Dually residuated lattice ordered semigroups.Math. Ann. 159 (1965), 105–114. Zbl 0138.02104, MR 0183797 |
| Reference:
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[16] K. L. N. Swamy: Dually residuated lattice ordered semigroups II.Math. Ann. 160 (1965), 64–71. MR 0191851, 10.1007/BF01364335 |
| Reference:
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[17] K. L. N. Swamy: Dually residuated lattice ordered semigroups III.Math. Ann. 167 (1966), 71–74. Zbl 0158.02601, MR 0200364, 10.1007/BF01361218 |
| . |
