Some distributivities in GBbi-QRs characterizing Boolean rings

• Autorzy: Joanna Kaleta
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

quasigroup; generalized Boolean bi-quasiring; generalized Boolean quasiring; Boolean ring; ring-like structure; axiomatic quantum mechanics; quantum logic

Kategorie tematyczne

• 16Y99: None of the above, but in this section
• 06E20: Ring-theoretic properties
• 03G25: Other algebras related to logic
• 03G12: Quantum logic
• 20N05: Loops, quasigroups
• 81P10: Logical foundations of quantum mechanics; quantum logic

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2004
• Tom: 24
• Numer: 1
• Strony: 115-124

Daty

wydano

2004

otrzymano

2003-12-09

poprawiono

2004-06-03

poprawiono

2004-06-11

Twórcy

autor

Joanna Kaleta

• Department of Applied Mathematics, Warsaw Agricultural University (WAU; SGGW), ul. Nowoursynowska 166, PL-02-766 Warsaw

Bibliografia

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• [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.

Identyfikatory

DOI

10.7151/dmgaa.1079