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Quotient structures in lattice effect algebras
Kybernetika, Tome 55 (2019) no. 5, pp. 879-895
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In this paper, we define some types of filters in lattice effect algebras, investigate some relations between them and introduce some new examples of lattice effect algebras. Then by using the strong filter, we find a CI-lattice congruence on lattice effect algebras, such that the induced quotient structure of it is a lattice effect algebra, too. Finally, under some suitable conditions, we get a quotient MV-effect algebra and a quotient orthomodular lattice, by this congruence relation.
In this paper, we define some types of filters in lattice effect algebras, investigate some relations between them and introduce some new examples of lattice effect algebras. Then by using the strong filter, we find a CI-lattice congruence on lattice effect algebras, such that the induced quotient structure of it is a lattice effect algebra, too. Finally, under some suitable conditions, we get a quotient MV-effect algebra and a quotient orthomodular lattice, by this congruence relation.
DOI : 10.14736/kyb-2019-5-0879
Classification : 06B10, 81R05
Keywords: Lattice effect algebra; CI-lattice; Sasaki arrow; (strong; fantastic; implicative; positive implicative) filter; Riesz ideal; D-ideal; MV-effect algebra; orthomodular lattice 
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Sharafi, Amir Hossein; Borzooei, Rajb Ali. Quotient structures in lattice effect algebras. Kybernetika, Tome 55 (2019) no. 5, pp. 879-895. doi: 10.14736/kyb-2019-5-0879

[1] Avallone, A., Vitolo, P.: Congruences and ideals of effect algebras. Kluwer Academic Publishers 20 (2003), 1, 67-77. | DOI | MR

[2] Bennett, M. K., Foulis, D. J.: Phi-symmetric effect algebras. Found. Physics 25 (1995), 12, 1699-1722. | DOI | MR

[3] Borzooei, R. A., Dvurečenskij, A., Sharafi, A. H.: Material implications in lattice effect algebras. Inform. Sci. 433-434 (2018), 233-240. | DOI | MR

[4] Borzooei, R. A., Shoar, S. Khosravi, Ameri, R.: Some types of filters in MTL-algebras. Fuzzy Sets Systems 187 (2012), 1, 92-102. | DOI | MR

[5] Chajda, I., Halaš, R., Kühr, J.: Many-valued quantum algebras. Algebra Univers. 60 (2009), 1, 63-90. | DOI | MR

[6] Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures. Springer Netherlands, 2000. | DOI | MR | Zbl

[7] Farahani, H., Zahiri, O.: Algebraic view of MTL-filters. Ann. Univ. Craiova 40 (2013), 1, 34-44. | MR

[8] Foulis, D. J.: MV and Hyting effect algebras. Found. Physics 30 (2000), 10, 1687-1706. | DOI | MR

[9] Foulis, D. J., Bennett, M. K.: Effect algebras and unsharp quantum logics. Found. Physics 24 (1994), 10, 1331-1352. | DOI | MR | Zbl

[10] Foulis, D. J., Pulmannová, S.: Logical connectives on lattice effect algebras. Studia Logica 100 (2012), 6, 1291-1315. | DOI | MR

[11] Haveshki, M., Saeid, A. Borumand, Eslami, E.: Some types of filters in BL-algebras. Soft Computing 10 (2006), 8, 657-664. | DOI

[12] Jenča, G., Marinová, I., Riečanová, Z.: Central elements, blocks and sharp elements of lattice effect algebras. In: Proc. Third Seminar Fuzzy Sets and Quantum Structures 2002, pp. 28-33.

[13] Jenča, G., Pulmannová, S.: Ideals and quotients in lattice ordered effect algebras. Soft Computing 5 (2001), 5, 376-380. | DOI

[14] Cignoli, R., D'Ottaviano, I. M. L., Mundici, D.: Algebraic Foundations of Many-Valued Reasoning. Springer Science and Business Media, 2000. | DOI | MR | Zbl

[15] Pulmannová, S., Vinceková, E.: Congruences and ideals in lattice effect algebras as basic algebras. Kybernetika 45 (2009), 6, 1030-1039. | MR

[16] Rad, S. Rafiee, Sharafi, A. H., Smets, S.: A Complete axiomatisation for the logic of lattice effect algebras. Int. J. Theoret. Physics (2019). | DOI

[17] Riečanová, Z.: Generalization of blocks for D-lattices and lattice-ordered effect algebras. Int. J. Theoret. Physics 39 (2000), 2, 231-237. | DOI | MR

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