Home Generalized Sasaki mappings in d0-Algebras
Article
Licensed
Unlicensed Requires Authentication

Generalized Sasaki mappings in d0-Algebras

  • Anna Avallone and Paolo Vitolo EMAIL logo
Published/Copyright: February 25, 2025
Become an author with De Gruyter Brill

Abstract

We define the notion of a generalized Sasaki mapping on a d0-algebra. We also introduce d0-algebras with the Sasaki property and, for such d0-algebras, we construct the generalized Sasaki projection, which turns out to be a generalized Sasaki mapping.

MSC 2010: 03G25; 06A12; 06F35
  1. (Communicated by Mirko Navara)

References

[1] Avallone, A.—Barbieri G.—Vitolo, P.: Hahn decomposition of modular measures and applications, Comment. Math. 43(2) (2003), 149–168.Search in Google Scholar

[2] Avallone, A.—Barbieri G.—Vitolo, P.—Weber, H.: Decomposition of effect algebras and the Hammer-Sobczyk theorem, Algebra Universalis 60(1) (2009), 1–18.10.1007/s00012-008-2083-zSearch in Google Scholar

[3] Avallone, A.—Barbieri G.—Vitolo, P.—Weber, H.: Modular d0-algebras, Boll. Unione Mat. Ital. 13 (2020), 529–538.10.1007/s40574-020-00237-6Search in Google Scholar

[4] Avallone, A.—De Simone, A.—Vitolo, P.: Effect algebras and extensions of measures, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 9(2) (2006), 423–444.Search in Google Scholar

[5] Avallone, A.—Vitolo, P.: Decomposition and control theorems on effect algebras, Sci. Math. Jpn. 58(1) (2003), 1–14.Search in Google Scholar

[6] Avallone, A.—Vitolo, P.: Lattice uniformities on effect algebras, Internat. J. Theoret. Phys. 44(7) (2005), 793–806.10.1007/s10773-005-7057-8Search in Google Scholar

[7] Avallone, A.—Vitolo, P.: Lyapunov decomposition of measures on effect algebras, Sci. Math. Jpn. 69(1) (2009), 79–87.Search in Google Scholar

[8] Avallone, A.—Vitolo, P.: Hahn decomposition in d0-algebras, Soft Comput. 23(22) (2019), 11373–11388.10.1007/s00500-019-04049-5Search in Google Scholar

[9] Avallone, A.—Vitolo, P.: Lyapunov decomposition in d0-algebras, Rend. Circ. Mat. Palermo (2) 69 (2020), 837–859.10.1007/s12215-019-00440-1Search in Google Scholar

[10] Avallone, A.—Vitolo, P.: The center of a d0-algebra, Rep. Math. Phys. 86(1) (2020), 63–78.10.1016/S0034-4877(20)30057-4Search in Google Scholar

[11] Avallone, A.—Vitolo, P.: Kalmbach measurability in d0-algebras, Math. Slovaca 72(6) (2022), 1387–1402.10.1515/ms-2022-0095Search in Google Scholar

[12] Avallone, A.—Vitolo, P.: Sharp elements in d0-algebras, Iran. J. Fuzzy Syst. 20(6) (2023), 85–103.10.1007/s00012-024-00871-7Search in Google Scholar

[13] Avallone, A.—Vitolo, P.: Decomposition of d0-algebras, submitted for publication.Search in Google Scholar

[14] Bennett, M. K.—Foulis, D. J.: Effect algebras and unsharp quantum logics, Found. Phys. 24(10) (1994), 1331–1352.10.1007/BF02283036Search in Google Scholar

[15] Bennett, M. K.—Foulis, D. J.: Phi-symmetric effect algebras, Found. Phys. 25(12) (1994), 1699–1722.10.1007/BF02057883Search in Google Scholar

[16] Bennett, M. K.—Foulis, D. J.: A generalized Sasaki projection for effect algebras, Tatra Mt. Math. Publ. 15 (1998), 55–66.Search in Google Scholar

[17] Chovanec, F.—Kôpka, F.: D-lattices, Internat. J. Theoret. Phys. 34 (1995), 1297–1302.10.1007/BF00676241Search in Google Scholar

[18] Constantinescu, C.: Some Properties of Spaces of Measures, Atti Sem. Mat. Fis. Univ. Modena, Vol. 35 (supplement), Modena, 1989.Search in Google Scholar

[19] Dvurečenskij, A.—Graziano, M. G.: Remarks on representations of minimal clans, Tatra Mt. Math. Publ. 15 (1998), 31–53.Search in Google Scholar

[20] Dvurečenskij, A.—Graziano, M. G.: On representations of commutative Bck-algebras, Demonstr. Math. 32(2) (1999), 227–246.10.1515/dema-1999-0202Search in Google Scholar

[21] Dvurečenskij, A.—Pulmannova, S.: New Trends in Quantum Structures. Mathematics and its Applications, Vol. 516, Kluwer Academic Publishers, Dordrecht, 2000.Search in Google Scholar

[22] Foulis, D. J.: A note on orthomodular lattices, Port. Math. 21(1) (1962), 65–72.Search in Google Scholar

[23] Gabriëls, J. J. M.—Gagola, S. M.—Navara, M.: Sasaki projections, Algebra Universalis 77(3) (2017), 305–320.10.1007/s00012-017-0428-1Search in Google Scholar

[24] Nakamura, M.: The permutability in a certain orthocomplemented lattice, Kodai Math. Sem. Rep. 9(4) (1957), 158–160.10.2996/kmj/1138843933Search in Google Scholar

[25] Rosa, M.—Vitolo, P.: Blocks and compatibility in d0-algebras, Algebra Universalis 78(4) (2017), 489–513.10.1007/s00012-017-0469-5Search in Google Scholar

[26] Rosa, M.—Vitolo, P.: Topologies and uniformities on d0-algebras, Math. Slovaca 67(6) (2017), 1301–1322.10.1515/ms-2017-0053Search in Google Scholar

[27] Rosa, M.—Vitolo, P.: Measures and submeasures on d0-algebras, Ric. Mat. 67 (2018), 373–386.10.1007/s11587-018-0379-7Search in Google Scholar

[28] Sasaki, U.: Orthocomplemented lattices satisfying the exchange axiom, J. Sci. Hiroshima Univ. Ser. A 17 (1954), 293–302.10.32917/hmj/1557281141Search in Google Scholar

[29] Schmidt, K. D.: Minimal clans: a class of ordered partial semigroups including Boolean rings and lattice-ordered groups. In: Semigroups, Theory and Applications (H. Jürgensen, G. Lallement and H. J. Weinert, eds.), Proceedings of a Conference held in Oberwolfach, 1986, Lecture Notes in Math., Vol. 1320, Springer, Berlin, 1988, pp. 300–341.10.1007/BFb0083442Search in Google Scholar

[30] Schmidt, K. D.: Jordan decompositions of generalized vector measures. In: Pitman Research Notes in Mathematics Series, Vol. 214, Longman Scientific & Technical, Harlow, 1989.Search in Google Scholar

[31] Vitolo, P.: A generalization of set-difference, Math. Slovaca 61(6) (2011), 835–850.10.2478/s12175-011-0051-0Search in Google Scholar

[32] Weber, H.: An abstraction of clans of fuzzy sets, Ric. Mat. 46(2) (1997), 457–472.Search in Google Scholar

[33] Wyler, O.: Clans, Compos. Math. 17 (1965), 172–189.10.1515/zpt-1965-0505Search in Google Scholar

Received: 2024-02-28
Accepted: 2024-09-18
Published Online: 2025-02-25
Published in Print: 2025-02-25

© 2025 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Generalized Sasaki mappings in d0-Algebras
  2. On a theorem of Nathanson on Diophantine approximation
  3. Constructing infinite families of number fields with given indices from quintinomials
  4. Partitions into two Lehmer numbers in ℤq
  5. Fundamental systems of solutions of some linear differential equations of higher order
  6. On k-Circulant matrices involving the Lucas numbers of even index
  7. Explicit formulae for the Drazin inverse of the sum of two matrices
  8. On nonoscillation of fractional order functional differential equations with forcing term and distributed delays
  9. Novel generalized tempered fractional integral inequalities for convexity property and applications
  10. Convergence of α-Bernstein-Durrmeyer operators about a collection of measures
  11. The problem of finding eigenvalues and eigenfunctions of boundary value problems for an equation of mixed type
  12. Orbital Hausdorff dependence and stability of the solution to differential equations with variable structure and non-instantaneous impulses
  13. Improvements on the Leighton oscillation theorem for second-order dynamic equations
  14. Topogenous orders on forms
  15. Comparison of topologies on fundamental groups with subgroup topology viewpoint
  16. An elementary proof of the generalized Itô formula
  17. Asymptotic normality for kernel-based test of conditional mean independence in Hilbert space
  18. Advancing reliability and medical data analysis through novel statistical distribution exploration
  19. Historical notes on the 75th volume of Mathematica Slovaca - Authors of the first issue from 1951
Downloaded on 30.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2025-0001/html
Scroll to top button