نتایج جستجو برای: semimodular lattice

تعداد نتایج: 93362  

2009
E. T. SCHMIDT

We present a new gluing construction for semimodular lattices, related to the Hall–Dilworth construction. The gluing constructions in the lattice theory started with a paper of M. Hall and R. P. Dilworth [4] to prove that there exists a modular lattice that cannot be embedded in any complemented modular lattice. This construction is the following: let K and L be lattices, let F be a filter of K...

2008
Gábor Czédli Tamás Schmidt

A semimodular lattice L of finite length will be called an almost-geometric lattice, if the order J(L) of its nonzero join-irreducible elements is a cardinal sum of at most two-element chains. We prove that each finite distributive lattice is isomorphic to the lattice of congruences of a finite almost-geometric lattice.

2008
G. GRÄTZER

We show that in a finite semimodular lattice, the ordering of joinirreducible congruences is done in a special type of sublattice, we call a tight S7.

Journal: :J. Comb. Theory, Ser. A 1995
Curtis D. Bennett Bruce E. Sagan

Stanley [18] introduced the notion of a supersolvable lattice, L, in part to combinatorially explain the factorization of its characteristic polynomial over the integers when L is also semimodular. He did this by showing that the roots of the polynomial count certain sets of atoms of the lattice. In the present work we define an object called an atom decision tree. The class of semimodular latt...

2009
GÁBOR CZÉDLI

A lattice L is said to satisfy (the lattice theoretic version of) Frankl’s conjecture if there is a join-irreducible element f ∈ L such that at most half of the elements x of L satisfy f ≤ x. Frankl’s conjecture, also called as union-closed sets conjecture, is well-known in combinatorics, and it is equivalent to the statement that every finite lattice satisfies Frankl’s conjecture. Let m denote...

2010
B. M. Vernikov

We describe G-sets whose congruences satisfy some natural lattice or multiplicative restrictions. In particular, we determine G-sets with distributive, arguesian, modular, upper or lower semimodular congruence lattice as well as congruence n-permutable G-sets for n = 2, 2.5, 3.

1997
J. B. NATION ALEX POGEL

For any ordered set P, the join dense completions of P form a complete lattice K(P) with least element O(P), the lattice of order ideals of P, and greatest element M(P), the Dedekind-MacNeille completion of P. The lattice K(P) is isomorphic to an ideal of the lattice of all closure operators on the lattice O(P). Thus it inherits some local structural properties which hold in the lattice of clos...

In this paper we investigate some properties of congruences on ternary semigroups. We also define the notion of congruence on a ternary semigroup generated by a relation and we determine the method of obtaining a congruence on a ternary semigroup T from a relation R on T. Furthermore we study the lattice of congruences on a ternary semigroup and we show that this lattice is not generally modular...

Journal: :Order 2012
Gábor Czédli

A finite lattice L is called slim if no three join-irreducible elements of L form an antichain. Slim semimodular lattices play the main role in G. Czédli and E.T. Schmidt [5], where lattice theory is applied to a purely group theoretical problem. Here we develop a unique matrix representation for these lattices.

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