论文信息 - Maximal Sublattices of Nite Distributive Lattices

Maximal Sublattices of Nite Distributive Lattices

Algebraic properties of lattices of quotients of nite posets are considered. Using the known duality between the category of all nite posets together with all order-preserving maps and the category of all nite distributive (0; 1)-lattices together with all (0; 1)-lattice ho-momorphisms, algebraic and arithmetic properties of maximal proper sublattices and, in particular, Frattini sublattices of nite distributive (0; 1)-lattices are thereby obtained.

M E Adams | J Schmid

[1] Ulrich Faigle,et al. On the complexity of interval orders and semiorders , 1987, Discret. Math..

[2] I. Rabinovitch,et al. The rank of a distributive lattice , 1979, Discret. Math..

[3] The Frattini sublattice of a distributive lattice , 1973 .

[4] Khee Meng Koh. On the Frattini sublattice of a lattice , 1971 .

[5] Peter C. Fishburn,et al. Posets with large dimension and relatively few critical pairs , 1993 .

[6] The Frattini sublattice of a finite distributive lattice , 1994 .

[7] K. M. Koh,et al. Frattini sublattices of distributive lattices , 1973 .

[8] William T. Trotter,et al. Dimension Theory for Ordered Sets , 1982 .

[9] Deciding Frattini is NP-complete , 1994 .

[10] E. T. Schmidt,et al. On ideal theory for lattices , 1958 .

[11] MAXIMAL SUBLATTICES AND FRATTINI SUBLATTICES OF BOUNDED LATTICES , 1997 .