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Coupled Right Orthosemirings Induced by Orthomodular Lattices

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L. P. Belluce, A. Di Nola and B. Gerla established a connection between MV-algebras and (dually) lattice ordered semirings by means of so-called coupled semirings. A similar connection was found for basic algebras and semilattice ordered right near semirings by the authors. The aim of this paper is to derive an analogous connection for orthomodular lattices and certain semilattice ordered near semirings via so-called coupled right orthosemirings.

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  1. Belluce, L. P., Di Nola, A., Ferraioli, A. R.: MV-semirings and their sheaf representations. Order 30, 165–179 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. Beran, L.: Orthomodular Lattices. Algebraic Approach. Reidel, Dordrecht (1985)

    Book  MATH  Google Scholar 

  3. Bruns, G., Harding, J.: Algebraic aspects of orthomodular lattices. Fund. Theories Phys. 111, 37–65 (2000). Kluwer, Dordrecht

    MathSciNet  MATH  Google Scholar 

  4. Chajda, I., Länger, H.: Commutative basic algebras and coupled near semirings. Soft Comput. 19, 1129–1134 (2015)

  5. Chajda, I., Länger, H.: A representation of basic algebras by coupled right near semirings. Acta Sci. Math. (Szeged) 81, 361–374 (2015)

  6. Di Nola, A., Gerla, B.: Algebras of Lukasiewicz’s logic and their semiring reducts. Contemp. Math. 377, 131–144 (2005). AMS, Providence, RI

    Article  MathSciNet  MATH  Google Scholar 

  7. Gerla, B.: Many-valued logic and semirings. Neural Netw. World 5, 467–480 (2003)

    Google Scholar 

  8. Golan, J. S.: The Theory of Semirings with Applications in Mathematics and Theoretical Computer Science. Longman, Harlow (1992)

    MATH  Google Scholar 

  9. Kalmbach, G.: Orthomodular Lattices. Academic Press, London (1983)

    MATH  Google Scholar 

  10. Kuich, W., Salomaa, A.: Semirings, Automata, Languages. Springer, Berlin (1986)

    Book  MATH  Google Scholar 

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Correspondence to Helmut Länger.

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Chajda, I., Länger, H. Coupled Right Orthosemirings Induced by Orthomodular Lattices. Order 34, 1–7 (2017).

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