Complements in modular and semimodular lattices.
Cyclic congruences of slim semimodular lattices and non-finite axiomatizability of some finite structures
We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among finite graphs. (This fact is a consequence of a general theorem proved by L. Ham and M. Jackson, and the counterpart of this fact for all bipartite graphs in the class of all graphs is a well-known consequence of the compactness theorem.) Also, to exemplify that our method is applicable in various fields of mathematics, we prove that neither finite simple groups, nor the...
Decompositions in lattices and some representations of algebras [Book]
Description combinatoire des ultramétriques
Finite groups with modular chains
In 1954, Kontorovich and Plotkin introduced the concept of a modular chain in a lattice to obtain a lattice-theoretic characterization of the class of torsion-free nilpotent groups. We determine the structure of finite groups with modular chains. It turns out that this class of groups lies strictly between the class of finite groups with lower semimodular subgroup lattice and the projective closure of the class of finite nilpotent groups.
Finite orders and their minimal strict completion lattices
Whereas the Dedekind-MacNeille completion D(P) of a poset P is the minimal lattice L such that every element of L is a join of elements of P, the minimal strict completion D(P)∗ is the minimal lattice L such that the poset of join-irreducible elements of L is isomorphic to P. (These two completions are the same if every element of P is join-irreducible). In this paper we study lattices which are minimal strict completions of finite orders. Such lattices are in one-to-one correspondence with finite...
Formality of the complements of subspace arrangements with geometric lattices.
Graph automorphisms and cells of lattices
In this paper we apply the notion of cell of a lattice for dealing with graph automorphisms of lattices (in connection with a problem proposed by G. Birkhoff).
Graph automorphisms of semimodular lattices
This paper deals with the relations between graph automorphisms and direct factors of a semimodular lattice of locally finite length.
Graph isomorphisms of semimodular lattices
Gruppen mit geometrischen Abschnitten im Untergruppenverband.
Homotopy and homology of finite lattices.
Ideal nil-extensions of semigroups with semimodular congruence lattices.
Independence in a set with orthogonality
Locally Projective-Planar Lattices which Satisfy the Bundle Theorem.
Meet and join within the lattice of set partitions.
Modular Substructures in Pseudomodular Lattices.
On a problem of Kertesz and Stern
On algebraic lattices and semisimple algebras
On central relations of complete lattices