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Orthorings

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Abstrakty
EN
Certain ring-like structures, so-called orthorings, are introduced which are in a natural one-to-one correspondence with lattices with 0 every principal ideal of which is an ortholattice. This correspondence generalizes the well-known bijection between Boolean rings and Boolean algebras. It turns out that orthorings have nice congruence and ideal properties.
Twórcy
autor
  • Palacký University, Olomouc, Department of Algebra and Geometry, Tomkova 40, 77900 Olomouc, Czech Republic
  • Vienna University of Technology, Institute of Discrete Mathematics and Geometry, Research Unit Algebra, Wiedner Hauptstraß e 8-10, 1040 Vienna, Austria
Bibliografia
  • [1] G. Birkhoff, Lattice Theory, third edition, AMS Colloquium Publ. 25, Providence, RI, 1979.
  • [2] I. Chajda, Pseudosemirings induced by ortholattices, Czechoslovak Math. J. 46 (1996), 405-411.
  • [3] I. Chajda and G. Eigenthaler, A note on orthopseudorings and Boolean quasirings, Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 207 (1998), 83-94.
  • [4] I. Chajda, G. Eigenthaler and H. Länger, Congruence Classes in Universal Algebra, Heldermann Verlag, Lemgo 2003.
  • [5] I. Chajda and H. Länger, Ring-like operations in pseudocomplemented semilattices, Discuss. Math. Gen. Algebra Appl. 20 (2000), 87-95.
  • [6] I. Chajda and H. Länger, Ring-like structures corresponding to MV-algebras via symmetric difference, Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, to appear.
  • [7] I. Chajda, H. Länger and M. Maczyński, Ring-like structures corresponding to generalized orthomodular lattices, Math. Slovaca 54 (2004), 143-150.
  • [8] G. Dorfer, A. Dvurecenskij and H. Länger, Symmetric difference in orthomodular lattices, Math. Slovaca 46 (1996), 435-444.
  • [9] D. Dorninger, H. Länger and M. Maczyński, The logic induced by a system of homomorphisms and its various algebraic characterizations, Demonstratio Math. 30 (1997), 215-232.
  • [10] D. Dorninger, H. Länger and M. Maczyński, On ring-like structures occurring in axiomatic quantum mechanics, Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 206 (1997), 279-289.
  • [11] D. Dorninger, H. Länger and M. Maczyński, On ring-like structures induced by Mackey's probability function, Rep. Math. Phys. 43 (1999), 499-515.
  • [12] D. Dorninger, H. Länger and M. Maczyński, Lattice properties of ring-like quantum logics, Intern. J. Theor. Phys. 39 (2000), 1015-1026.
  • [13] D. Dorninger, H. Länger and M. Maczyński, Concepts of measures on ring-like quantum logics, Rep. Math. Phys. 47 (2001), 167-176.
  • [14] D. Dorninger, H. Länger and M. Maczyński, Ring-like structures with unique symmetric difference related to quantum logic, Discuss. Math. General Algebra Appl. 21 (2001), 239-253.
  • [15] G. Grätzer, General Lattice Theory, second edition, Birkhäuser Verlag, Basel 1998.
  • [16] J. Hedlíková, Relatively orthomodular lattices, Discrete Math. 234 (2001), 17-38.
  • [17] M. F. Janowitz, A note on generalized orthomodular lattices, J. Natur. Sci. Math. 8 (1968), 89-94.
  • [18] H. Länger, Generalizations of the correspondence between Boolean algebras and Boolean rings to orthomodular lattices, Tatra Mt. Math. Publ. 15 (1998), 97-105.
  • [19] H. Werner, A Mal'cev condition for admissible relations, Algebra Universalis 3 (1973), 263.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1081
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