Ring-like structures corresponding to generalized orthomodular lattices

Ivan Chajda; Helmut Länger; Maciej Mączyński

Mathematica Slovaca (2004)

  • Volume: 54, Issue: 2, page 143-150
  • ISSN: 0232-0525

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Chajda, Ivan, Länger, Helmut, and Mączyński, Maciej. "Ring-like structures corresponding to generalized orthomodular lattices." Mathematica Slovaca 54.2 (2004): 143-150. <http://eudml.org/doc/34592>.

@article{Chajda2004,
author = {Chajda, Ivan, Länger, Helmut, Mączyński, Maciej},
journal = {Mathematica Slovaca},
keywords = {generalized orthomodular lattice; Boolean pseudoring; arithmetical; congruence regular; distributive; associative; Boolean ring},
language = {eng},
number = {2},
pages = {143-150},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Ring-like structures corresponding to generalized orthomodular lattices},
url = {http://eudml.org/doc/34592},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Chajda, Ivan
AU - Länger, Helmut
AU - Mączyński, Maciej
TI - Ring-like structures corresponding to generalized orthomodular lattices
JO - Mathematica Slovaca
PY - 2004
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 54
IS - 2
SP - 143
EP - 150
LA - eng
KW - generalized orthomodular lattice; Boolean pseudoring; arithmetical; congruence regular; distributive; associative; Boolean ring
UR - http://eudml.org/doc/34592
ER -

References

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  2. CHAJDA I., Pseudosemirings induced by ortholattices, Czechoslovak Math. J. 46 (1996), 405-411. (1996) Zbl0879.06003MR1408295
  3. CHAJDA I.-EIGENTHALER G., A note on orthopseudorings and Boolean quasirings, Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 207 (1998), 83-94. (1998) Zbl1040.06003MR1749914
  4. CHAJDA I.-LÄNGER H., Ring-like operations in pseudocomplemented semilattices, Discuss. Math. Gen. Algebra Appl. 20 (2000), 87-95. Zbl0968.06004MR1782088
  5. DILWORTH R. P., The structure of relatively complemented lattices, Ann. of Math. (2) 51 (1950), 348-359. (1950) Zbl0036.01802MR0033795
  6. DORFER G., Some properties of congruence relations on orthomodular lattices, Discuss. Math. Gen. Algebra Appl. 21 (2001), 57-66. Zbl1011.06011MR1868617
  7. DORNINGER D.-LÄNGER H.-MACZYNSKI M., The logic induced by a system of homomorphisms and its various algebraic characterizations, Demonstratio Math. 30 (1997), 215-232. (1997) Zbl0879.06005MR1446613
  8. DORNINGER D.-LÄNGER H.-MACZYNSKI M., On ring-like structures occurring in axiomatic quantum mechanics, Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 206 (1997), 279-289. (1997) MR1632939
  9. DORNINGER D.-LÄNGER H.-MACZYNSKI M., On ring-like structures induced by Mackey's probability function, Rep. Math. Phys. 43 (1999), 499-515. (1999) Zbl1056.81004MR1713402
  10. DORNINGER D.-LÄNGER H.-MACZYNSKI M., Lattice properties of ring-like quantum logics, Internat. J. Theoret. Phys. 39 (2000), 1015-1026. Zbl0967.03055MR1779170
  11. DORNINGER D.-LÄNGER H.-M4CZYNSKI M., Concepts of measures on ring-like quantum logics, Rep. Math. Phys. 47 (2001), 167-176. Zbl0980.81009MR1836328
  12. DORNINGER D.-LÄNGER H.-MACZYNSKI M., Ring-like structures with unique symmetric difference related to quantum logic, Discuss. Math. Gen. Algebra Appl. 21 (2001), 239-253. Zbl1014.81003MR1894319
  13. JANOWITZ M. F., A note on generalized orthomodular lattices, J. Natur. Sci. Math. 8 (1968), 89-94. (1968) Zbl0169.02104MR0231762
  14. KALMBACH G., Orthomodular Lattices, Academic Press, London, 1983. (1983) Zbl0528.06012MR0716496
  15. LÄNGER H., Generalizations of the correspondence between Boolean algebras and Boolean rings to orthomodular lattices, Tatra Mt. Math. Publ. 15 (1998), 97-105. (1998) Zbl0939.03075MR1655082
  16. PTÁK P.-PULMANNOVÁ S., Orthomodular Structures as Quantum Logics, Kluwer Acad. Publ., Dordrecht, 1991. (1991) Zbl0743.03039MR1176314

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