Maximal completion of a pseudo MV-algebra
Archivum mathematicum, Tome 39 (2003) no. 2, pp. 141-161
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In the present paper we investigate the relations between maximal completions of lattice ordered groups and maximal completions of pseudo $MV$-algebras.
In the present paper we investigate the relations between maximal completions of lattice ordered groups and maximal completions of pseudo $MV$-algebras.
Classification : 06B23, 06D35, 06F15
Keywords: pseudo $MV$-algebra; maximal completion; $b$-atomicity; directproduct
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Jakubík, Ján. Maximal completion of a pseudo MV-algebra. Archivum mathematicum, Tome 39 (2003) no. 2, pp. 141-161. http://geodesic.mathdoc.fr/item/ARM_2003_39_2_a4/

[1] Černák, Š.: On the maximal Dedekind completion of a lattice ordered group. Math. Slovaca 29 (1979), 305–313. | MR

[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

[3] Conrad, P.: Lattice Ordered Groups. Tulane University, 1970. | Zbl

[4] Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum structures. Kluwer Academic Publishers, Dordrecht-Boston-London, and Ister Science, Bratislava, 2000. | MR

[5] Dvurečenskij, A.: Pseudo $MV$-algebras are intervals in $\ell $-groups. J. Austral. Math. Soc. (to appear).

[6] Everett, C. J.: Sequence completion of lattice modules. Duke Math. J. 11 (1994), 109–119. | MR

[7] Fuchs, L.: Paritally Ordered Algebraic Systems. Pergamon Press, Oxford-New York-London-Paris, 1963. | MR

[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

[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

[10] Jakubík, J.: Maximal Dedekind completion of an abelian lattice ordered group. Czechoslovak Math. J. 28 (1978), 611–631. | MR

[11] Jakubík,J.: Direct product decompositions of $MV$-algebras. Czechoslovak Math. J. 44 (1994), 725–739.

[12] Jakubík, J.: Complete generators and maximal completions of $MV$-algebras. Czechoslovak Math. J. 48 (1998), 597–608. | MR

[13] Jakubík, J.: Basic elements in a pseudo $MV$-algebra. Soft Computing (to appear). | MR

[14] Jakubík, J.: Direct product decompositions of pseudo $MV$-algebras. Archivum Math. (to appear). | MR

[15] Jakubík, J.: Strong subdirect products of $MV$-algebras. (Submitted).

[16] Rachůnek, J.: A noncommutative generalization of $MV$-algebras. Czechoslovak Math. J. 25 (2002), 255–273.