A cover-preserving embedding of semimodular lattices into geometric lattices
نویسندگان
چکیده
منابع مشابه
Cover preserving embedding of modular lattices into partition lattices
Wild, M., Cover preserving embedding of modular lattices into partition lattices, Discrete Mathematics 112 (1993) 207-244. When is a finite modular lattice couer preserving embeddable into a partition lattice? We give some necessary, and slightly sharper sufficient conditions. For example, the class of cover preserving embeddable modular lattices strictly contains the class of acyclic modular l...
متن کاملCover-preserving Embedding of Modular Lattices
In this note we prove: If a subdirect product of ̄nitely many ̄nite projective geometries has the cover-preserving embedding property, then so does each factor. In what follows all the lattices will be ̄nite modular ones. A ̄nite lattice K has the cover-preseving embedding property, abbreviated as CPEP with respect a variety V of lattices if whenever K can be embedded into a ̄nite lattice L in ...
متن کاملCongruence-preserving Extensions of Finite Lattices to Semimodular Lattices
We prove that every finite lattice has a congruence-preserving extension to a finite semimodular lattice.
متن کاملCongruence Lattices of Finite Semimodular Lattices
We prove that every finite distributive lattice can be represented as the congruence lattice of a finite (planar) semimodular lattice.
متن کاملA Construction of Semimodular Lattices
In this paper we prove that if !.l' is a finite lattice. and r is an integral valued function on !.l' satisfying some very natural then there exists a finite geometric (that is.• semimodular and atomistic) lattice containing asa sublatticesuch that r !.l'restricted to Sf. Moreover. we show that if, for all intervals of. semimodular lattices of length at most r(e) are given. then can be chosen t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2010
ISSN: 0001-8708
DOI: 10.1016/j.aim.2010.05.001