## Convex chains in a pseudo MV-algebra.(English)Zbl 1014.06010

Summary: For a pseudo MV-algebra $$\mathcal A$$ we denote by $$\ell (\mathcal A)$$ the underlying lattice of $$\mathcal A$$. In the present paper we investigate the algebraic properties of maximal convex chains in $$\ell (\mathcal A)$$ containing the element 0. We generalize a result of A. Dvurečenskij and S. Pulmannová.

### MSC:

 06D35 MV-algebras
Full Text:

### References:

 [1] R. Cignoli, M. I. D’Ottaviano and D. Mundici: Algebraic Foundations of Many-Valued Reasoning, Trends in Logic, Studia Logica Library, vol. 7. Kluwer Academic Publishers, Dordrecht, 2000. [2] P. Conrad: Lattice Ordered Groups. Tulane University, 1970. · Zbl 0258.06011 [3] A. Dvurečenskij and S. Pulmannová: New Trends in Quantum Structures. Kluwer Academic Publishers, Dordrecht, and Ister Science, Bratislava, 2000. · Zbl 0987.81005 [4] G. Georgescu and A. Iorgulescu: Pseudo $$MV$$-algebras: a noncommutative extension of $$MV$$-algebras. The Proceedings of the Fourth International Symposyium on Economic Informatics, Bucharest, 1999, pp. 961-968. · Zbl 0985.06007 [5] G. Georgescu and A. Iorgulescu: Pseudo $$MV$$-algebras. Multiple Valued Logic (a special issue dedicated to Gr. C. Moisil) 6 (2001), 95-135. · Zbl 1014.06008 [6] J. Jakubík: Direct product of $$MV$$-algebras. Czechoslovak Math. J. 44(119) (1994), 725-739. · Zbl 0821.06011 [7] J. Jakubík: Direct product decompositions of pseudo $$MV$$-algebras. Arch. Math. 37 (2001), 131-142. · Zbl 1070.06003 [8] J. Jakubík: On chains in $$MV$$-algebras. Math. Slovaca 51 (2001), 151-166. · Zbl 0988.06008 [9] J. Rachůnek: A non-commutative generalization of $$MV$$-algebras. Czechoslovak Math. J. 52(127) (2002), 255-273. · Zbl 1012.06012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.