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2020 | 49 | 3 | 269-290
Tytuł artykułu

Module Structure on Effect Algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, by considering the notions of effect algebra and product effect algebra, we define the concept of effect module. Then we investigate some properties of effect modules, and we present some examples on them. Finally, we introduce some topologies on effect modules.  
Rocznik
Tom
49
Numer
3
Strony
269-290
Opis fizyczny
Daty
wydano
2020-11-04
Twórcy
  • Farhangian University Department of Mathematics Tehran, Iran
  • Shahid Beheshti University Department of Mathematics Tehran, Iran
Bibliografia
  • [1] M. K. Bennett, D. J. Foulis, Phi-symmetric effect algebras, Foundations of Physics, vol. 25 (1995), pp. 1699–1722, DOI: http://dx.doi.org/10.1007/BF02057883
  • [2] R. A. Borzooei, A. Dvurečenskij, A. H. Sharafi, Material Implications in Lattice Effect Algebras, Information Sciences, vol. 433–434 (2018), pp. 233–240, DOI: http://dx.doi.org/10.1016/j.ins.2017.12.049
  • [3] R. A. Borzooei, S. S. Goraghani, Free Extended BCK-Module, Iranian Journal of Mathematical Science and Informatics, vol. 10(2) (2015), pp. 29–43, DOI: http://dx.doi.org/10.7508/ijmsi.2015.02.004
  • [4] R. A. Borzooei, S. S. Goraghani, Free MV-modules, Journal of Intelligent and Fuzzy System, vol. 31(1) (2016), pp. 151–161, DOI: http://dx.doi.org/10.3233/IFS-162128
  • [5] R. A. Borzooei, N. Kohestani, G. R. Rezaei, Metrizability on (Semi)topological BL-algebra, Soft Computing, vol. 16(10) (2012), pp. 1681–1690, DOI: http://dx.doi.org/10.1007/s00500-012-0852-2
  • [6] R. A. Borzooei, G. R. Rezaei, N. Kohestani, On (semi)topological BL-algebra, Iranian Journal of Mathematical Science and Informatics, vol. 6(1) (2011), pp. 59–77, DOI: http://dx.doi.org/10.7508/ijmsi.2011.01.006
  • [7] R. A. Borzooei, O. Zahiri, Topology on BL-algebras, Fuzzy Sets and Systems, vol. 289 (2016), pp. 137–150, DOI: http://dx.doi.org/10.1016/j.fss.2014.11.014
  • [8] R. Cignoli, I. M. L. D'Ottaviano, D. Mundici, Algebraic Foundations of Many-valued Reasoning, Kluwer Academic-Dordrecht (2000).
  • [9] A. Di Nola, P. Flondor, I. Leustean, MV-modules, Journal of Algebra, vol. 267 (2003), pp. 21–40, DOI: http://dx.doi.org/10.1016/S0021-8693(03)00332-6
  • [10] A. Di Nola, C. Russo, Semiring and semimodules issues in MV-algebras, Communications in Algebra, vol. 41(3) (2013), pp. 1017–1048, DOI: http://dx.doi.org/10.1080/00927872.2011.610074
  • [11] A. Dvurečenskij, New trends in quantum structures, Kluwer Academic/Ister Science-Dordrecht/Bratislava (2000).
  • [12] A. Dvurečenskij, Product effect algebras, International Journal of Theoretical Physics, vol. 41(10) (2002), pp. 193–215, DOI: http://dx.doi.org/10.1023/A:1021017905403
  • [13] A. Dvurečenskij, States on Pseudo effect algebras and integrals, Foundations of Physics, vol. 41 (2011), pp. 1143–1162, DOI: http://dx.doi.org/10.1007/s10701-011-9537-4
  • [14] A. Dvurečenskij, T. Vetterlein, Pseudo effect algebras. II. Group represetation, International Journal of Theoretical Physics, vol. 40 (2001), pp. 703–726, DOI: http://dx.doi.org/10.1023/A:1004144832348
  • [15] F. Forouzesh, E. Eslami, A. B. Saeid, Spectral topology on MV-modules, New Mathematics and Natural Computation, vol. 11(1) (2015), pp. 13–33, DOI: http://dx.doi.org/10.1142/S1793005715500027
  • [16] D. J. Foulis, M. K. Bennett, Effect algebras and unsharp quantum logics, Foundations of Physics, vol. 24(10) (1994), pp. 1331–1352, DOI: http://dx.doi.org/10.1007/BF02283036
  • [17] S. S. Goraghani, R. A. Borzooei, Results on Prime Ideals in PMV-algebras and MV-modules, Italian Journal of Pure and Applied Mathematics, vol. 37 (2017), pp. 183–196.
  • [18] M. R. Rakhshani, R. A. Borzooei, G. R. Rezaei, On topological effect algebras, Italian Journal of Pure and Applied Mathematics, vol. 39 (2018), pp. 312–325.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_18778_0138-0680_2020_17
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