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Finite atomistic lattices that can be represented as lattices of quasivarieties

K. Adaricheva, Wiesław Dziobiak, V. Gorbunov (1993)

Fundamenta Mathematicae

We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].

Finite closed coverings of compact quantum spaces

Piotr M. Hajac, Atabey Kaygun, Bartosz Zieliński (2012)

Banach Center Publications

We consider the poset of all non-empty finite subsets of the set of natural numbers, use the poset structure to topologise it with the Alexandrov topology, and call the thus obtained topological space ℙ ∞ the universal partition space. Then we show that it is a classifying space for finite closed coverings of compact quantum spaces in the sense that any such a covering is functorially equivalent to a sheaf over this partition space. In technical terms, we prove that the category of finitely supported...

Finite groups with globally permutable lattice of subgroups

C. Bagiński, A. Sakowicz (1999)

Colloquium Mathematicae

The notions of permutable and globally permutable lattices were first introduced and studied by J. Krempa and B. Terlikowska-Osłowska [4]. These are lattices preserving many interesting properties of modular lattices. In this paper all finite groups with globally permutable lattices of subgroups are described. It is shown that such finite p-groups are exactly the p-groups with modular lattices of subgroups, and that the non-nilpotent groups form an essentially larger class though they have a description...

Finite groups with modular chains

Roland Schmidt (2013)

Colloquium Mathematicae

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

Gabriela Hauser Bordalo, Bernard Monjardet (2003)

Discussiones Mathematicae - General Algebra and Applications

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...

Finite topological spaces.

Juan A. Navarro González (1990)

Extracta Mathematicae

We show that the study of topological T0-spaces with a finite number of points agrees essentially with the study of polyhedra, by means of the geometric realization of finite spaces. In this paper all topological spaces are assumed to be T0.

Finitely generated almost universal varieties of 0 -lattices

Václav Koubek, Jiří Sichler (2005)

Commentationes Mathematicae Universitatis Carolinae

A concrete category 𝕂 is (algebraically) universal if any category of algebras has a full embedding into 𝕂 , and 𝕂 is almost universal if there is a class 𝒞 of 𝕂 -objects such that all non-constant homomorphisms between them form a universal category. The main result of this paper fully characterizes the finitely generated varieties of 0 -lattices which are almost universal.

Finitely valued f -modules, an addendum

Stuart A. Steinberg (2001)

Czechoslovak Mathematical Journal

In an ℓ -group M with an appropriate operator set Ω it is shown that the Ω -value set Γ Ω ( M ) can be embedded in the value set Γ ( M ) . This embedding is an isomorphism if and only if each convex ℓ -subgroup is an Ω -subgroup. If Γ ( M ) has a.c.c. and M is either representable or finitely valued, then the two value sets are identical. More generally, these results hold for two related operator sets Ω 1 and Ω 2 and the corresponding Ω -value sets Γ Ω 1 ( M ) and Γ Ω 2 ( M ) . If R is a unital ℓ -ring, then each unital ℓ -module over R is an f -module...

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