대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제15권3호
  • /
  • Pages.511-519
  • /
  • 2000
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

A NOTE ON JANOWITZ'S HULLS OF GENERALIZED ORTHOMODULAR LATTICES

  • 발행 : 2000.09.01
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초록

If G is a strict generalized orthomodular lattice and H={I｜I=[0, $\chi$, $\chi$$\in$G}, then H is prime ideal of the Janowitz's hull J(G) of G. If f is the janowitz's embedding, then the set of all commutatiors of f(G) equals the set of all commutators of the Janowitz's hull J(G) of G. Let L be an OML. Then L J(G) for a strict GOML G if and only if ther exists a proper nonprincipal prime ideal G in L.

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참고문헌

  1. Amer. Math. Soc. Colloq. Publ. v.25 Lattice Theory(3rd ed.) Birkhoff, G.
  2. Orthomodular Lattices Beran, L.
  3. J. Natur. Sci. and Math. v.8 A Note on Generalized Orhomodular Lattices Janowitz, M.
  4. Orthomodular Lattices Kalmbach, G.
  5. Pacific J. Math. v.14 Atomic orthocomplemented lattices MacLaren, M.
  6. Grundl. Math. Wiss. Theory of Symmetric Lattices Maeda, F.;Maeda, S.
  7. Introduction to Lattice Szasz, G.