Some distributivities in GBbi-QRs characterizing Boolean rings

Joanna Kaleta

Discussiones Mathematicae - General Algebra and Applications (2004)

  • Volume: 24, Issue: 1, page 115-124
  • ISSN: 1509-9415

Abstract

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This paper presents some manner of characterization of Boolean rings. These algebraic systems one can also characterize by means of some distributivities satisfied in GBbi-QRs.

How to cite

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Joanna Kaleta. "Some distributivities in GBbi-QRs characterizing Boolean rings." Discussiones Mathematicae - General Algebra and Applications 24.1 (2004): 115-124. <http://eudml.org/doc/287654>.

@article{JoannaKaleta2004,
abstract = {This paper presents some manner of characterization of Boolean rings. These algebraic systems one can also characterize by means of some distributivities satisfied in GBbi-QRs.},
author = {Joanna Kaleta},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {quasigroup; generalized Boolean bi-quasiring; generalized Boolean quasiring; Boolean ring; ring-like structure; axiomatic quantum mechanics; quantum logic; Boolean rings},
language = {eng},
number = {1},
pages = {115-124},
title = {Some distributivities in GBbi-QRs characterizing Boolean rings},
url = {http://eudml.org/doc/287654},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Joanna Kaleta
TI - Some distributivities in GBbi-QRs characterizing Boolean rings
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2004
VL - 24
IS - 1
SP - 115
EP - 124
AB - This paper presents some manner of characterization of Boolean rings. These algebraic systems one can also characterize by means of some distributivities satisfied in GBbi-QRs.
LA - eng
KW - quasigroup; generalized Boolean bi-quasiring; generalized Boolean quasiring; Boolean ring; ring-like structure; axiomatic quantum mechanics; quantum logic; Boolean rings
UR - http://eudml.org/doc/287654
ER -

References

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  1. [1] I. Chajda, Pseudosemirings induced by ortholattices, Czechoslovak Math. J. 46 (1996), 405-411. Zbl0879.06003
  2. [2] I. Chajda and G. Eigenthaler, A note on orthopseudorings and Boolean quasirings, Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 207 (1998), 83-94. Zbl1040.06003
  3. [3] G. Dorfer, A. Dvurecenskij and H. Länger, Symmetric difference in orthomodular lattices, Math. Slavaca 46 (1996). doi: 435-444 Zbl0890.06006
  4. [4] D. Dorninger, Sublogics of ring-like quantum logics, Tatra Mt. Math. Publ. 15 (1998), 75-83. Zbl0939.03074
  5. [5] D. Dorninger, H. Länger and M. Maczyński, The logic induced by system of homomorphisms and its various algebraic characterizations, Demonstratio Math. 30 (1997), 215-232. Zbl0879.06005
  6. [6] D. Dorninger, H. Länger and M. Maczyński, On ring-like structures occurring in axiomatic quantum mechanics, Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 206 (1997), 279-289. Zbl0945.03095
  7. [7] D. Dorninger, H. Länger and M. Maczyński, Lattice properties of ring-like quantum logics, Internat. J. Theoret. Phys. 39 (2000), 1015-1026. Zbl0967.03055
  8. [8] D. Dorninger, H. Länger and M. Maczyński, On ring-like structures induced by Mackey's probability function, Rep. Math. Phys. 43 (1999), 499-515. Zbl1056.81004
  9. [9] H. Länger, Generalizations of the correspondence between Boolean algebras and Boolean rings to orthomodular lattices, Tatra Mt. Math. Publ. 15 (1998), 97-105. Zbl0939.03075
  10. [10] H.O. Pflugfelder, Quasigroups and Loops: Introduction, Heldermann Verlag, Berlin 1990. Zbl0715.20043

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