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Subcentral Ideals in Generalized Effect Algebras

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Abstract

In this paper, we introduce subcentral ideals in the class of cancellative positivepartial abelian monoids (CPAMs). Every complementary pair of subcentral idealsin a CPAM P corresponds to a subdirect decomposition of P. If this decompositionis direct, the corresponding ideals are called central. Subcentral ideals arecharacterized as central elements in the lattice of the recently introducedso-called R 1-ideals. Every subcentral ideal is a central element in the lattice of allideals. A subcentral ideal I is central iff I is Riesz ideal. In an upper-directedCPAM, every subcentral ideal is central.

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REFERENCES

  1. Chevalier, G., and Pulmannov, S. Some ideal lattices in Partial Abelian Monoids, preprint.

  2. Foulis, D., and Bennett, M. K., Effect algebras and unsharp quantum logics, Found. Phys. 24 (1994) 1331-1352.

    Google Scholar 

  3. Giuntini, R., and Greuling, H., Toward a formal language for unsharp properties, Found. Phys. 19 (1994) 769-780.

    Google Scholar 

  4. Grätzer, G. Universal Algebra, 2nd ed., Springer-Verlag, Berlin (1979), pp. 80-81.

    Google Scholar 

  5. Greechie, R., Foulis, D., and Pulmannová, S. The center of an effect algebra, Order 12 (1995) 91-106.

    Google Scholar 

  6. Gudder, S., and Pulmannová, S., Quotients of partial abelian monoids, Algebra Univers. 38 (1998) 395-421.

    Google Scholar 

  7. Kalmbach, G., and Riečanová, Z. An axiomatization for abelian relative inverses, Dem. Math. 27 (1994) 684-699.

    Google Scholar 

  8. Kôpka, F., and Chovanec, F., D-posets, Math. Slovaca 44 (1994) 21-34.

    Google Scholar 

  9. Maeda, F., and Maeda, S., Theory of Symmetric Lattices, Springer-Verlag, Berlin, (1970), pp. 18-19.

    Google Scholar 

  10. Pulmannová, S., Congruences in partial abelian semigroups, Algebra Univers. 37 (1997) 119-140.

    Google Scholar 

  11. Wilce, W., Partial abelian semigroups, Int. J. Theor. Phys. 34 (1995) 1807-1812.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Electrical Engineering and Informatics, Slovak Technical University, I 812 19, Bratislava, Slovakia

    Gejza Jenčs

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  1. Gejza Jenčs
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Jenčs, G. Subcentral Ideals in Generalized Effect Algebras. International Journal of Theoretical Physics 39, 745–755 (2000). https://doi.org/10.1023/A:1003610426013

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