About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Pulmannová, Silvia ; Vinceková, Elena
Congruences and ideals in lattice effect algebras as basic algebras. (English). Kybernetika, vol. 45 (2009), issue 6, pp. 1030-1039
MSC: 03G12, 06C15, 08A55, 81P10 | MR 2650081 | Zbl 1200.62055
Keywords:
basic algebra; effect algebra; ideal; congruence
Summary:
Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.
References:
[1] A. Avallone and P. Vitolo: Congruences and ideals of effect algebras. Order 20 (2003), 67–77. MR 1993411
[2] I. Chajda, R. Halaš, and J. Kühr: Many valued quantum algebras. Alg. Univ. 60 (2009), 63–90. MR 2480632
[3] C. C. Chang: Algebraic analysis of many valued logics. Trans. Amer. Math. Soc. 88 (1958), 467–490. MR 0094302 | Zbl 0084.00704
[4] F. Chovanec and F. Kôpka: Boolean D-posets. Tatra Mt. Math. Publ. 10 (1997), 1–15. MR 1469294
[5] A. Dvurečenskij and S. Pulmannová: New Trends in Quantum Structures. Kluwer Academic Publishers, Dordrecht 2000. MR 1861369
[6] D. Foulis and M. K. Bennett: Effect algebras and unsharp quantum logics. Found. Phys. 24 (1994), 1331–1352. MR 1304942
[7] R. Giuntini: Quantum MV-algebras. Studia Logica 56 (1996), 303–417. MR 1397488 | Zbl 1093.06011
[8] S. Gudder: Total extensions of effect algebras. Found. Phys. Lett. 8 (1995), 243–252. MR 1339403
[9] G. Jenča and S. Pulmannová: Ideals and quotients in lattice ordered effect albebras. Soft Computing 5 (2001), 376–380.
[10] F. Kôpka and F. Chovanec: D-posets. Math. Slovaca 44 (1994), 21–34. MR 1290269
Partner of
EuDML logo