Previous |  Up |  Next

Article

Keywords:
pseudo $MV$-algebra; maximal completion; $b$-atomicity; directproduct
Summary:
In the present paper we investigate the relations between maximal completions of lattice ordered groups and maximal completions of pseudo $MV$-algebras.
References:
[1] Černák, Š.: On the maximal Dedekind completion of a lattice ordered group. Math. Slovaca 29 (1979), 305–313. MR 0561629
[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
[3] Conrad, P.: Lattice Ordered Groups. Tulane University, 1970. Zbl 0258.06011
[4] Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum structures. Kluwer Academic Publishers, Dordrecht-Boston-London, and Ister Science, Bratislava, 2000. MR 1861369
[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 0009592
[7] Fuchs, L.: Paritally Ordered Algebraic Systems. Pergamon Press, Oxford-New York-London-Paris, 1963. MR 0171864
[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
[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
[10] Jakubík, J.: Maximal Dedekind completion of an abelian lattice ordered group. Czechoslovak Math. J. 28 (1978), 611–631. MR 0506435
[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 1637863
[13] Jakubík, J.: Basic elements in a pseudo $MV$-algebra. Soft Computing (to appear). MR 1901010
[14] Jakubík, J.: Direct product decompositions of pseudo $MV$-algebras. Archivum Math. (to appear). MR 1838410
[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.
Partner of
EuDML logo