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Blocks and compatibility in \({{\rm d}_0}\)-algebras

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Abstract

The structure of \({{\rm d}_0}\)-algebra is a generalization of a D-lattice. We extend to this structure the definitions of compatible elements and blocks, and investigate their properties.

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References

  1. Chajda I., Halaš R., Kühr J.: Many-valued quantum algebras. Algebra Universalis 60, 63–90 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chovanec F., Kôpka F.: Boolean D-posets. Tatra Mt. Math. Publ. 10, 183–197 (1997)

    MATH  MathSciNet  Google Scholar 

  3. Constantinescu, C.: Some properties of spaces of measures. Atti Sem. Mat. Fis. Univ. Modena 35(suppl.), 1–286 (1989)

  4. Dvurečenskij, A., Graziano, M.G.: Remarks on representations of minimal clans. Tatra Mt. Math. Publ. 15, 31–53 (1998). Quantum structures, II (Liptovský Ján, 1998)

  5. Dvurečenskij A., Graziano M.G.: On representations of commutative BCK-algebras. Demonstratio Math. 32, 227–246 (1999)

    MATH  MathSciNet  Google Scholar 

  6. Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures. Kluwer Academic Publishers, Dordrecht (2000)

  7. Iséki K.: Algebraic formulations of propositional calculi. Proc. Japan Acad. 41, 803–807 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  8. Iséki K.: An algebra related with a propositional calculus. Proc. Japan Acad. 42, 26–29 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  9. Jenča G., Pulmannová S.: Ideals and quotients in lattice ordered effect algebras. Soft Comput. 5, 376–380 (2001)

    Article  MATH  Google Scholar 

  10. Kalmbach, G.: Orthomodular lattices. London Mathematical Society Monographs, vol. 18. Academic Press, Inc., London (1983)

  11. Riečanová Z.: Generalization of blocks for D-lattices and lattice-ordered effect algebras. Internat. J. Theoret. Phys. 39, 231–237 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  12. Rosa, M., Vitolo, P.: Topologies and uniformities on \({{\rm d}_0}\)-algebras. Math. Slovaca (in press)

  13. Rosa, M., Vitolo, P.: Measures and submeasures on \({{\rm d}_0}\)-algebras. (2016, submitted)

  14. Schmidt, K.D.: Minimal clans: a class of ordered partial semigroups including Boolean rings and lattice-ordered groups. In: Semigroups, theory and applications (Oberwolfach, 1986). Lecture Notes in Math., vol. 1320, pp. 300–341. Springer, Berlin (1988)

  15. Schmidt, K.D.: Jordan decompositions of generalized vector measures. Pitman Research Notes in Mathematics Series, vol. 214. Longman Scientific & Technical, Harlow (1989)

  16. Tkadlec J.: Distributivity and associativity in effect algebras. Fuzzy Sets and Systems 289, 151–156 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  17. Vitolo P.: A generalization of set-difference. Math. Slovaca 61, 835–850 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  18. Weber H.: An abstraction of clans of fuzzy sets. Ricerche Mat. 46, 457–472 (1997)

    MATH  MathSciNet  Google Scholar 

  19. Wyler O.: Clans. Compositio Math. 17, 172–189 (1965)

    MATH  MathSciNet  Google Scholar 

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Correspondence to Paolo Vitolo.

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Presented by S. Pulmannova.

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Rosa, M., Vitolo, P. Blocks and compatibility in \({{\rm d}_0}\)-algebras. Algebra Univers. 78, 489–513 (2017). https://doi.org/10.1007/s00012-017-0469-5

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  • DOI: https://doi.org/10.1007/s00012-017-0469-5

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