Lattices respecting convex decompositions, I

• Autorzy: Beran L. , Saarimäki M.
• Języki publikacji: EN

Abstrakty

EN

We prove the following results: Let (L1 L2) be a convex decomposition of a lattice L. If L1 and L2 are 0-modular, then L is 0-modular. If L1 is 0-distributive (or L1 is distributive with 0) and L2 is distributive (or L2 is 0-distributive), then L is 0-distributive.

Słowa kluczowe

EN

convex decomposition; 0-modular

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 2
• Strony: 217--224
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Beran L.

• Department of Algebra, Charles University, Sokolovská 83, 18600 Prague 8, Czech Republic

autor

Saarimäki M.

• Department of Mathematics, University of Jyväskylä, P. O. Box 35, Fin - 40351 Jyväskylä, Finland

Bibliografia

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• [2] L. Beran, Orthomodular Lattices. Algebraic Approach, Reidel, Dordrecht, 1984.
• [3] L. Beran, Distributivity via Boolean algebras, Atti Sem. Mat. Fis. Univ. Modena 48 (2000), 191-206.
• [4] G. Grätzer, General Lattice Theory, 2nd ed., Birkhäuser Verlag, Basel, 1998.
• [5] P. A. Grillet, J. C. Varlet, Complementedness conditions in lattices, Bull. Soc. Roy. Sei. Liège 36 (1967), 628-642.
• [6] M. Hall, R. P. Dilworth, The imbedding problem for modular lattices, Annals Math. 45 (1944), 450-456.
• [7] C. Herrmann, S-verklebte Summen von Verbänden, Math. Z. 130 (1973), 255-274.
• [8] J. E. McLaughlin, Atomic lattices with unique comparable complements, Proc. Amer. Math. Soc. 7 (1956), 864-866.
• [9] Y. Rav, Semiprime ideals in general lattices, J. Pure Appl. Algebra 56 (1989), 105-118.
• [10] M. Saarimäki, Disjointness of lattice elements, Math. Nachrichten 159 (1992), 169-174.
• [11] M. Saarimäki, Disjointness and complementedness in upper continuous lattices, University of Jyväskylä, Report 78 (1998).
• [12] Z. Tian, π-inverse semigroups whose lattice of n-inverse subsemigroups is 0-distributive or 0-modular, Semigroup Forum 56 (1998), 334-338.
• [13] J. C. Varlet, A generalization of the notion of pseudo-complementedness, Bull. Soc. Roy. Sci. Liège 36 (1968), 149-158.