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.
(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
© 2025 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Generalized Sasaki mappings in d0-Algebras
- On a theorem of Nathanson on Diophantine approximation
- Constructing infinite families of number fields with given indices from quintinomials
- Partitions into two Lehmer numbers in ℤq
- Fundamental systems of solutions of some linear differential equations of higher order
- On k-Circulant matrices involving the Lucas numbers of even index
- Explicit formulae for the Drazin inverse of the sum of two matrices
- On nonoscillation of fractional order functional differential equations with forcing term and distributed delays
- Novel generalized tempered fractional integral inequalities for convexity property and applications
- Convergence of α-Bernstein-Durrmeyer operators about a collection of measures
- The problem of finding eigenvalues and eigenfunctions of boundary value problems for an equation of mixed type
- Orbital Hausdorff dependence and stability of the solution to differential equations with variable structure and non-instantaneous impulses
- Improvements on the Leighton oscillation theorem for second-order dynamic equations
- Topogenous orders on forms
- Comparison of topologies on fundamental groups with subgroup topology viewpoint
- An elementary proof of the generalized Itô formula
- Asymptotic normality for kernel-based test of conditional mean independence in Hilbert space
- Advancing reliability and medical data analysis through novel statistical distribution exploration
- Historical notes on the 75th volume of Mathematica Slovaca - Authors of the first issue from 1951
Articles in the same Issue
- Generalized Sasaki mappings in d0-Algebras
- On a theorem of Nathanson on Diophantine approximation
- Constructing infinite families of number fields with given indices from quintinomials
- Partitions into two Lehmer numbers in ℤq
- Fundamental systems of solutions of some linear differential equations of higher order
- On k-Circulant matrices involving the Lucas numbers of even index
- Explicit formulae for the Drazin inverse of the sum of two matrices
- On nonoscillation of fractional order functional differential equations with forcing term and distributed delays
- Novel generalized tempered fractional integral inequalities for convexity property and applications
- Convergence of α-Bernstein-Durrmeyer operators about a collection of measures
- The problem of finding eigenvalues and eigenfunctions of boundary value problems for an equation of mixed type
- Orbital Hausdorff dependence and stability of the solution to differential equations with variable structure and non-instantaneous impulses
- Improvements on the Leighton oscillation theorem for second-order dynamic equations
- Topogenous orders on forms
- Comparison of topologies on fundamental groups with subgroup topology viewpoint
- An elementary proof of the generalized Itô formula
- Asymptotic normality for kernel-based test of conditional mean independence in Hilbert space
- Advancing reliability and medical data analysis through novel statistical distribution exploration
- Historical notes on the 75th volume of Mathematica Slovaca - Authors of the first issue from 1951