Orthomodular Posets Can Be Organized as Conditionally Residuated Structures

Ivan Chajda; Helmut LÄNGER

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2014)

  • Volume: 53, Issue: 2, page 29-33
  • ISSN: 0231-9721

Abstract

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It is proved that orthomodular posets are in a natural one-to-one correspondence with certain residuated structures.

How to cite

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Chajda, Ivan, and LÄNGER, Helmut. "Orthomodular Posets Can Be Organized as Conditionally Residuated Structures." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 53.2 (2014): 29-33. <http://eudml.org/doc/262173>.

@article{Chajda2014,
abstract = {It is proved that orthomodular posets are in a natural one-to-one correspondence with certain residuated structures.},
author = {Chajda, Ivan, LÄNGER, Helmut},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Orthomodular poset; partial commutative groupoid with unit; conditionally residuated structure; divisibility condition; orthogonality condition; orthomodular posets; conditionally residuated structures},
language = {eng},
number = {2},
pages = {29-33},
publisher = {Palacký University Olomouc},
title = {Orthomodular Posets Can Be Organized as Conditionally Residuated Structures},
url = {http://eudml.org/doc/262173},
volume = {53},
year = {2014},
}

TY - JOUR
AU - Chajda, Ivan
AU - LÄNGER, Helmut
TI - Orthomodular Posets Can Be Organized as Conditionally Residuated Structures
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2014
PB - Palacký University Olomouc
VL - 53
IS - 2
SP - 29
EP - 33
AB - It is proved that orthomodular posets are in a natural one-to-one correspondence with certain residuated structures.
LA - eng
KW - Orthomodular poset; partial commutative groupoid with unit; conditionally residuated structure; divisibility condition; orthogonality condition; orthomodular posets; conditionally residuated structures
UR - http://eudml.org/doc/262173
ER -

References

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  8. Kalmbach, G., Orthomodular Lattices, Academic Press, London, 1983. (1983) Zbl0528.06012MR0716496
  9. Matoušek, M., Pták, P., 10.1007/s11083-008-9102-8, Order 26 (2009), 1–21. (2009) Zbl1201.06006MR2487165DOI10.1007/s11083-008-9102-8
  10. Navara, M., Characterization of state spaces of orthomodular structures, In: Proc. Summer School on Real Analysis and Measure Theory, Grado, Italy, (1997), 97–123. (1997) 
  11. Pták, P., 10.1090/S0002-9939-98-04403-7, Proc. Amer. Math. Soc. 126 (1998), 2039–2046. (1998) Zbl0894.06003MR1452822DOI10.1090/S0002-9939-98-04403-7
  12. Pták, P., Pulmannová, S., Orthomodular Structures as Quantum Logics, Kluwer, Dordrecht, 1991. (1991) MR1176314

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