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On duality between order and algebraic structures in Boolean systems

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Języki publikacji
EN
Abstrakty
EN
We present an extension of the known one-to-one correspondence between Boolean algebras and Boolean rings with unit being two types of Boolean systems endowed with order and algebraic structures, respectively. Two equivalent generalizations of Boolean algebras are discussed. We show that there is a one-to-one correspondence between any of the two mentioned generalized Boolean algebras and Boolean rings without unit.
Rocznik
Tom
Strony
35--62
Opis fizyczny
Bibliogr. 45 poz.
Twórcy
autor
  • Institute of Mathematics, University of Rzeszow, ul. Rejtana 16A, 35-310 Rzeszow, Poland
autor
  • Institute of Mathematics, University of Rzeszow, ul. Rejtana 16A, 35-310 Rzeszow, Poland
Bibliografia
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  • [8] F. Chovanec, F. Kôpka, D-posets, In: K. Engesser, D. M. Gabbay, D. Lehmann (eds.), Handbook of Quantum Logic and Quantum Structures: Quantum Structures, 367-428, Elsevier, Amstredam, 2007.
  • [9] A. Dadej, K. Halik, Properties of di erences in B-rings, J. Math. Appl. 34 (2011), 5-13.
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  • [12] D. Dorninger, H. Länger, M. Mączyński, On ring-like structures induced by Mackey's probability function, Rep. Math. Phys. 43 (1999), 499-515.
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  • [14] D. Dorninger, H. Länger, M. Mączyński, Concepts of measures on ring-like quantum logics, Rep. Math. Phys. 47 (2001), 167-176.
  • [15] D. Dorninger, H. Länger, M. Mączyński, Ring-like structures with unique symmetric di erence related to quantum logic, Discuss. Math. Gen. Algebra Appl. 21 (2001), 239-253.
  • [16] R. Frič, Remarks on statistical maps and fuzzy (operational) random variables, Tatra Mt. Math. Publ. 30 (2005), 21-34.
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  • [30] F. Kôpka, D-posets of fuzzy sets, Tatra Mt. Math. Publ. 1 (1992), 83-87.
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  • [34] M. Papčo, On fuzzy random variables: examples and generalizations, Tatra Mt. Math. Publ. 30 (2005), 175-185.
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  • [45] D. A. Vladimirov, Boolean Algebras, Nauka, Moscow 1969 (in Russian).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f26520e0-6625-4ff2-811e-c4fbffdafce6
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