George Grätzer started writing his General Lattice Theory in 1968. It was published in 1978.
It set out “to discuss in depth the basics of general lattice theory.” Almost 900 exercises, 193 …

While the study of planar lattices goes back to the 1970s (KA Baker, PC Fishburn, and FS
Roberts [20] and D. Kelly and I. Rival [223]), a systematic study of planar semimodular …

Each finite closure system, whence each finite lattice, can be described in terms of"
implicational bases"(called" covers of functional dependencies" in relational database …

Extending former results by G. Grätzer and EW Kiss (1986)[5] and M. Wild (1993)[9] on finite
(upper) semimodular lattices, we prove that each semimodular lattice L of finite length has a …

In 1980, U. Faigle introduced a sort of finite geometries on posets that are in bijective
correspondence with finite semimodular lattices. His result has almost been forgotten in …

NOTES ON PLANAR SEMIMODULAR LATTICES. V. COVER-PRESERVING EMBEDDINGS
OF FINITE SEMIMODULAR LATTICES INTO SIMPLE SEMIMODULAR LATT Page 1 NOTES …

It is not known which finite graphs occur as induced subgraphs of a hypercube. This is
relevant in the theory of parallel computing. The ordered version of the problem is: Which …

In 2008, László Zádori proved that the lattice S ub (V) of all subspaces of a vector space V of
finite dimension at least 3 over a finite field F has a 5-element generating set; in other words …

A lattice is said to be finite height generated if it is complete and every element is the join of
some elements of finite height. Extending former results by Grätzer and Kiss (Order 2: 351 …

Some recent results on semimodular lattices are surveyed, and some related results are
given. The topics include a strong form of the Jordan-Hölder theorem, the semimodularity of …