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1982 news about orthomodular lattices. (English) Zbl 0554.06009

In this note new results found for ortholattices between 1980 and 1984 are presented in a very readable form. The announced books by G. Kalmbach, Orthomodular Lattices (1983; Zbl 0512.06011), and L. Beran, Orthomodular Lattices (1985), have appeared.
Reviewer: D.Schweigert

MSC:

06C15 Complemented lattices, orthocomplemented lattices and posets

Keywords:

ortholattices

Citations:

Zbl 0512.06011
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References:

[1] Beltrametti, E.; Cassinelli, G., The Logic of Quantum Mechanics, (Encycl. Math., 15 (1981), Addison-Wesley: Addison-Wesley Reading) · Zbl 0595.03062
[2] Beran, L., Central and exchange properties of orthomodular lattices, Math. Nachr., 97, 247-251 (1980) · Zbl 0452.06009
[3] Beran, L., Extension of a theorem of Gudder und Schelp to polynomials of orthomodular lattices, (Proc. AMS, 81 (1981)), 518-520 · Zbl 0458.06006
[4] Bruns, G., Varieties of modular ortholattices (1981), McMaster Univ.,, Preprint · Zbl 0518.06007
[5] Bruns, G.; Greechie, R., Orthomodular lattices which can be covered by finitely many blocks (1981), McMaster Univ.,: McMaster Univ., KSU, Preprint · Zbl 0493.06008
[6] Davey, B. A.; Werner, H., Dualities and equivalences for varieties of algebras (1981), Univ. Kassel, Preprint
[7] Dichtl, M., There are loops of order three in orthomodular lattices, Arch. Math. (Basel), 37, 285-286 (1981) · Zbl 0473.06006
[8] M. Dichtl, Astroids and pastings, Alg. Universalis, to appear.; M. Dichtl, Astroids and pastings, Alg. Universalis, to appear.
[9] Dietz, U., Orthomodular orthogonalities (1982), Univ. Ulm, Preprint
[10] Dorninger, D., A note on lattice operations between observables in axiomatic quantum mechanics (1981), T. Univ. Wien, Preprint · Zbl 0584.03043
[11] R. Godowski, Varieties of orthomodular lattices with a strongly full set of states, Demonstratio Math., to appear.; R. Godowski, Varieties of orthomodular lattices with a strongly full set of states, Demonstratio Math., to appear. · Zbl 0483.06007
[12] Godowski, R., States on orthomodular lattices (1981), T.U. Warszawa, Preprint · Zbl 0522.06010
[13] Godowski, R.; Greechie, R., Some equations related to states on orthomodular lattices (1982), T.U. Warzawa: T.U. Warzawa KSU, Preprint
[14] Goldblatt, R., Orthomodularity is not elementary (1982), Univ. Wellington, Preprint · Zbl 0593.03042
[15] (Halperin, I., Memoirs AMS, 34 (1981)), 252
[16] Hermann, C., A finitely generated modular ortholattice, Canad. Math. Bull., 24, 241-243 (1981) · Zbl 0457.06006
[17] Iturrioz, L., A representation theory for orthomodular lattices by means of closure spaces (1980), Univ. Lyon, Preprint
[18] L. Iturrioz, A simple proof of a characterization of complete, orthocomplemented lattices, Bull. London Math. Soc., to appear.; L. Iturrioz, A simple proof of a characterization of complete, orthocomplemented lattices, Bull. London Math. Soc., to appear. · Zbl 0476.06008
[19] Kalmbach, G., Orthomodular Lattices (1983), Academic Press: Academic Press London · Zbl 0512.06011
[20] Maeda, S., Lattice Theory and Quantum Logic (in Japanese) (1980), Maki-shoten: Maki-shoten Tokyo
[21] von Neumann, J., Continuous geometries with a transition probability, (Halperin, I., Memoirs AMS, 34 (1981)), 252 · Zbl 0479.46050
[22] Schulte Mönting, J., Cut elimination and word problems for varieties of lattices, Alg. Universalis, 12, 290-321 (1981) · Zbl 0528.03029
[23] Schweigert, D., Compatible relations of modular and orthomodular lattices, (Proc. AMS, 81 (1981)), 462-464 · Zbl 0458.06005
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