Some distributivities in GBbi-QRs characterizing Boolean rings
Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 1, pp. 115-124.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: quasigroup, generalized Boolean bi-quasiring, generalized Boolean quasiring, Boolean ring, ring-like structure, axiomatic quantum mechanics, quantum logic
@article{DMGAA_2004_24_1_a7,
     author = {Kaleta, Joanna},
     title = {Some distributivities in {GBbi-QRs} characterizing {Boolean} rings},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {115--124},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2004_24_1_a7/}
}
TY  - JOUR
AU  - Kaleta, Joanna
TI  - Some distributivities in GBbi-QRs characterizing Boolean rings
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2004
SP  - 115
EP  - 124
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2004_24_1_a7/
LA  - en
ID  - DMGAA_2004_24_1_a7
ER  - 
%0 Journal Article
%A Kaleta, Joanna
%T Some distributivities in GBbi-QRs characterizing Boolean rings
%J Discussiones Mathematicae. General Algebra and Applications
%D 2004
%P 115-124
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2004_24_1_a7/
%G en
%F DMGAA_2004_24_1_a7
Kaleta, Joanna. Some distributivities in GBbi-QRs characterizing Boolean rings. Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 1, pp. 115-124. http://geodesic.mathdoc.fr/item/DMGAA_2004_24_1_a7/

[1] I. Chajda, Pseudosemirings induced by ortholattices, Czechoslovak Math. J. 46 (1996), 405-411.

[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.

[3] G. Dorfer, A. Dvurecenskij and H. Länger, Symmetric difference in orthomodular lattices, Math. Slavaca 46 (1996). doi: 435-444

[4] D. Dorninger, Sublogics of ring-like quantum logics, Tatra Mt. Math. Publ. 15 (1998), 75-83.

[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.

[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.

[7] D. Dorninger, H. Länger and M. Maczyński, Lattice properties of ring-like quantum logics, Internat. J. Theoret. Phys. 39 (2000), 1015-1026.

[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.

[9] H. Länger, Generalizations of the correspondence between Boolean algebras and Boolean rings to orthomodular lattices, Tatra Mt. Math. Publ. 15 (1998), 97-105.

[10] H.O. Pflugfelder, Quasigroups and Loops: Introduction, Heldermann Verlag, Berlin 1990.