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Title: Maximal completion of a pseudo MV-algebra (English)
Author: Jakubík, Ján
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 39
Issue: 2
Year: 2003
Pages: 141-161
Summary lang: English
Category: math
Summary: In the present paper we investigate the relations between maximal completions of lattice ordered groups and maximal completions of pseudo $MV$-algebras. (English)
Keyword: pseudo $MV$-algebra
Keyword: maximal completion
Keyword: $b$-atomicity
Keyword: directproduct
MSC: 06B23
MSC: 06D35
MSC: 06F15
idZBL: Zbl 1108.06006
idMR: MR1994570
Date available: 2008-06-06T22:41:31Z
Last updated: 2012-05-10
Stable URL:
Reference: [1] Černák, Š.: On the maximal Dedekind completion of a lattice ordered group.Math. Slovaca 29 (1979), 305–313. MR 0561629
Reference: [2] Cignoli, R., D’Ottaviano, M. I., Mundici, D.: Algebraic Foundations of many-valued Reasoning.Trends in Logic, Studia Logica Library Vol. 7, Kluwer Academic Publishers, Dordrecht, 2000. MR 1786097
Reference: [3] Conrad, P.: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011
Reference: [4] Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum structures.Kluwer Academic Publishers, Dordrecht-Boston-London, and Ister Science, Bratislava, 2000. MR 1861369
Reference: [5] Dvurečenskij, A.: Pseudo $MV$-algebras are intervals in $\ell $-groups.J. Austral. Math. Soc. (to appear).
Reference: [6] Everett, C. J.: Sequence completion of lattice modules.Duke Math. J. 11 (1994), 109–119. MR 0009592
Reference: [7] Fuchs, L.: Paritally Ordered Algebraic Systems.Pergamon Press, Oxford-New York-London-Paris, 1963. MR 0171864
Reference: [8] Georgescu, G., Iorgulescu, A.: Pseudo $MV$-algebras: a noncommutative extension of $MV$--algebras.The Proceedings of the Fourth International Symposium on Economic Informatics, Romania, 1999, pp. 961–968. MR 1730100
Reference: [9] Georgescu, G., Iorgulescu, A.: Pseudo $MV$-algebras.Multiple Valued Logic (a special issue dedicated to Gr. Moisil) vol. 6, 2001, pp. 95–135. MR 1817439
Reference: [10] Jakubík, J.: Maximal Dedekind completion of an abelian lattice ordered group.Czechoslovak Math. J. 28 (1978), 611–631. MR 0506435
Reference: [11] Jakubík,J.: Direct product decompositions of $MV$-algebras.Czechoslovak Math. J. 44 (1994), 725–739.
Reference: [12] Jakubík, J.: Complete generators and maximal completions of $MV$-algebras.Czechoslovak Math. J. 48 (1998), 597–608. MR 1637863
Reference: [13] Jakubík, J.: Basic elements in a pseudo $MV$-algebra.Soft Computing (to appear). MR 1901010
Reference: [14] Jakubík, J.: Direct product decompositions of pseudo $MV$-algebras.Archivum Math. (to appear). MR 1838410
Reference: [15] Jakubík, J.: Strong subdirect products of $MV$-algebras.(Submitted).
Reference: [16] Rachůnek, J.: A noncommutative generalization of $MV$-algebras.Czechoslovak Math. J. 25 (2002), 255–273.


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