On centrally symmetric graphs
In this note we extend results on the covering graphs of modular lattices (Zelinka) and semimodular lattices (Gedeonova, Duffus and Rival) to the covering graph of certain graded lattices.
On complemented strong lattices
On distances and metrics in discrete ordered sets
Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality and restrictions of the distance to finite chains may or may not coincide with the natural, difference-of-height distance measured in a chain. It is shown that for semilattices the semimodularity ensures the good behaviour of the distances considered. The Jordan-Dedekind chain condition, which is weaker than semimodularity, is equivalent to the...
On forbidden configuration of pseudomodular lattices
We characterize the pseudomodular lattices by means of a forbidden configuration.
On interval decomposition lattices
Intervals in binary or n-ary relations or other discrete structures generalize the concept of interval in an ordered set. They are defined abstractly as closed sets of a closure system on a set V, satisfying certain axioms. Decompositions are partitions of V whose blocks are intervals, and they form an algebraic semimodular lattice. Lattice-theoretical properties of decompositions are explored, and connections with particular types of intervals are established.
On semimodular lattices of generating systems
On strong semimodular lattices III
On The Essential Flats Of Geometric Lattices
On the essential of geometric lattices.
On the Kurosh-Ore replacement property
Reducing the lengths of slim planar semimodular lattices without changing their congruence lattices
Following G. Grätzer and E. Knapp (2007), a slim planar semimodular lattice, SPS lattice for short, is a finite planar semimodular lattice having no as a sublattice. An SPS lattice is a slim rectangular lattice if it has exactly two doubly irreducible elements and these two elements are complements of each other. A finite poset is said to be JConSPS-representable if there is an SPS lattice such that is isomorphic to the poset of join-irreducible congruences of . We prove that if and...
Relations between some dimensions of semimodular lattices
The aim of this paper is to present relations between Goldie, hollow and Kurosh-Ore dimensions of semimodular lattices. Relations between Goldie and Kurosh-Ore dimensions of modular lattices were studied by Grzeszczuk, Okiński and Puczyłowski.
Riduzioni omotopicamente invarianti di insiemi parzialmente ordinati
Semimodularity in lower continuous strongly dually atomic lattices
For lattices of finite length there are many characterizations of semimodularity (see, for instance, Grätzer [3] and Stern [6]–[8]). The present paper deals with some conditions characterizing semimodularity in lower continuous strongly dually atomic lattices. We give here a generalization of results of paper [7].
Semimodularity of the Congruence Lattice on Regular ...-Semigroups.
Some remarks on modularity in prealgebraic and algebraic lattices
Structure des demi-groupes dont le treillis des sous-demi-groupes est semi-modulaire
Subgraph isomorphism in planar graphs and related problems.
Ternary spaces, media, and Chebyshev sets
The lattice of -subalgebras of a bounded distributive lattice