Extension of a theorem of Gudder and Schelp to polynomials of orthomodular lattices
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- by Ladislav Beran PDF
- Proc. Amer. Math. Soc. 81 (1981), 518-520 Request permission
Abstract:
Consider a polynomial expression $p(b,c, \ldots ,d) = e$ where any two of the elements $b,c, \ldots ,d$ commute. If an element $a$ commutes with $e$, then $b$ commutes with $p(a,c, \ldots ,d)$.References
- Garrett Birkhoff, Lattice Theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. 25, American Mathematical Society, New York, N. Y., 1948. MR 0029876
- Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
- George Grätzer, Lattice theory. First concepts and distributive lattices, W. H. Freeman and Co., San Francisco, Calif., 1971. MR 0321817
- R. J. Greechie, On the structure of orthomodular lattices satisfying the chain condition, J. Combinatorial Theory 4 (1968), 210–218. MR 227056
- S. P. Gudder and R. H. Schelp, Coordinatization of orthocomplemented and orthomodular posets, Proc. Amer. Math. Soc. 25 (1970), 229–237. MR 258690, DOI 10.1090/S0002-9939-1970-0258690-3
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 518-520
- MSC: Primary 06C15
- DOI: https://doi.org/10.1090/S0002-9939-1981-0601720-4
- MathSciNet review: 601720