Abstract
This paper is devoted to a general investigation of congruences and ideals in effect algebras. One of our main results is the existence of an order isomorphism between Riesz congruences and Riesz ideals. We also answer an open question of Dvurečenskij and Pulmannová by showing that an ideal is a Riesz ideal if and only if it is closed under generalized Sasaki projections.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Beltrametti, E. G. and Cassinelli, G.: The Logic of Quantum Mechanics, Addison-Wesley, Reading, Mass., 1981.
Bennet, M. K. and Foulis, D. J.: Effect algebras and unsharp quantum logics, Found. Phys. 24(10) (1994), 1331–1352.
Butnariu, D. and Klement, P.: Triangular Norm-based Measures and Games with Fuzzy Coalitions, Kluwer Acad. Publ., Dordrecht, 1993.
Chevalier, G. and Pulmannová, S.: Some ideal lattices in partial Abelian monoids and effect algebras, Order 17(1) (2000), 72–92.
Dvurečenskij, A. and Pulmannová, S.: New Trends in Quantum Structures, Kluwer Acad. Publ., Dordrecht, 2000.
Epstein, L. G. and Zhang, J.: Subjective probabilities on subjectively unamibguous events, Econometrica 69(2) (2001), 265–306.
Gudder, S. and Pulmannová, S.: Quotient of partial Abelian monoids, Algebra Universalis 38 (1997), 395–421.
Jenča, G. and Pulmannová, S.: Ideals and quotients in lattice ordered effect algebras, Preprint, 2000.
Kalmbach, G.: Orthomodular Lattices, Academic Press, London, 1983.
Riečanová, Z.: Compatibility and central elements in effect algebras, Tatra Mountains Math. Publ. 16 (1999), 151–158.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Avallone, A., Vitolo, P. Congruences and Ideals of Effect Algebras. Order 20, 67–77 (2003). https://doi.org/10.1023/A:1024458125510
Issue Date:
DOI: https://doi.org/10.1023/A:1024458125510