The Role of Halaš Identity in Orthomodular Lattices

Ivan Chajda

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

  • Volume: 53, Issue: 1, page 19-24
  • ISSN: 0231-9721

Abstract

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We prove that a certain identity introduced by R. Halaš for classifying basic algebras can be used for characterizing orthomodular lattices in the class of ortholattices with antitone involutions on every principal filter.

How to cite

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Chajda, Ivan. "The Role of Halaš Identity in Orthomodular Lattices." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 53.1 (2014): 19-24. <http://eudml.org/doc/261957>.

@article{Chajda2014,
abstract = {We prove that a certain identity introduced by R. Halaš for classifying basic algebras can be used for characterizing orthomodular lattices in the class of ortholattices with antitone involutions on every principal filter.},
author = {Chajda, Ivan},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {ortholattice; orthomodular lattice; antitone involution; principal filter; basic algebra; orthomodular lattices; basic algebras; ortholattices},
language = {eng},
number = {1},
pages = {19-24},
publisher = {Palacký University Olomouc},
title = {The Role of Halaš Identity in Orthomodular Lattices},
url = {http://eudml.org/doc/261957},
volume = {53},
year = {2014},
}

TY - JOUR
AU - Chajda, Ivan
TI - The Role of Halaš Identity in Orthomodular Lattices
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2014
PB - Palacký University Olomouc
VL - 53
IS - 1
SP - 19
EP - 24
AB - We prove that a certain identity introduced by R. Halaš for classifying basic algebras can be used for characterizing orthomodular lattices in the class of ortholattices with antitone involutions on every principal filter.
LA - eng
KW - ortholattice; orthomodular lattice; antitone involution; principal filter; basic algebra; orthomodular lattices; basic algebras; ortholattices
UR - http://eudml.org/doc/261957
ER -

References

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  1. Beran, L., Orthomodular Lattices – Algebraic Approach, Academia & D. Reidel Publ. Comp, Praha & Dordrecht, 1984. (1984) MR0785005
  2. Chajda, I., Basic algebras and their applications, an overview, In: Proc. of the Salzburg Conference AAA81, Contributions to General Algebra 20, Verlag J. Heyn, Klagenfurt, 2011, 1–10. (2011) MR2908429
  3. Chajda, I., 10.7151/dmgaa.1149, Discuss. Math., General Algebra Appl. 29 (2009), 21–33. (2009) Zbl1194.06005MR2598600DOI10.7151/dmgaa.1149
  4. Chajda, I., Halaš, R., Kühr, J., Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged) 71 (2005), 19–33. (2005) Zbl1099.06006MR2160352
  5. Chajda, I., Halaš, R., Kühr, J., 10.1007/s00012-008-2086-9, Algebra Universalis 60 (2009), 63–90. (2009) Zbl1219.06013MR2480632DOI10.1007/s00012-008-2086-9
  6. Chajda, I., Halaš, R., Kühr, J., Semilattice Structures, Heldermann Verlag, Lemgo, Germany, 2007. (2007) Zbl1117.06001MR2326262
  7. Kalmbach, G., Orthomodular Lattices, Academic Press, London–New York, 1983. (1983) Zbl0528.06012MR0716496

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