| Title:
|
Normalization of $MV$-algebras (English) |
| Author:
|
Chajda, I. |
| Author:
|
Halaš, R. |
| Author:
|
Kühr, J. |
| Author:
|
Vanžurová, A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
130 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
283-300 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider algebras determined by all normal identities of $MV$-algebras, i.e. algebras of many-valued logics. For such algebras, we present a representation based on a normalization of a sectionally involutioned lattice, i.e. a $q$-lattice, and another one based on a normalization of a lattice-ordered group. (English) |
| Keyword:
|
$MV$-algebra |
| Keyword:
|
abelian lattice-ordered group |
| Keyword:
|
$q$-lattice |
| Keyword:
|
normalization of a variety |
| MSC:
|
06D05 |
| MSC:
|
06D35 |
| MSC:
|
06F20 |
| MSC:
|
08B20 |
| idZBL:
|
Zbl 1112.06012 |
| idMR:
|
MR2164658 |
| DOI:
|
10.21136/MB.2005.134099 |
| . |
| Date available:
|
2009-09-24T22:21:18Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134099 |
| . |
| Reference:
|
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| Reference:
|
[2] Chang, C. C.: 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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| Reference:
|
[4] Cignoli, R.: Free lattice-ordered abelian groups and varieties of $MV$-algebras.Proc. IX. Latin. Amer. Symp. Math. Logic, Part 1, Not. Log. Mat. 38 (1993), 113–118. Zbl 0827.06012, MR 1332526 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[7] Chajda, I.: Congruence properties of algebras in nilpotent shifts of varieties.General Algebra and Discrete Mathematics (K. Denecke, O. Lüders, eds.), Heldermann, Berlin, 1995, pp. 35–46. Zbl 0821.08009, MR 1336150 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[10] Chajda, I., Halaš, R., Kühr, J.: Distributive lattices with sectionally antitone involutions.(to appear). MR 2160352 |
| Reference:
|
[11] Mel’nik, I. I.: Nilpotent shifts of varieties.Math. Notes 14 (1973), 692–696. (Russian) MR 0366782 |
| Reference:
|
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| Reference:
|
[13] Mundici, D.: $MV$-algebras are categorically equivalent to bouded commutative $BCK$- algebras.Math. Japon. 31 (1986), 889–894. MR 0870978 |
| Reference:
|
[14] Rachůnek, J.: $MV$-algebras are categorically equivalent to a class of ${DRl}_{1(i)}$-semigroups.Math. Bohem. 123 (1998), 437–441. MR 1667115 |
| . |
