Equipped graphs and modular lattices attached to them
Examples of statisch and finite-statisch AC-lattices
Exotic logics
Extensions dans les treillis
Filters in partially ordered sets
Finite groups with globally permutable lattice of subgroups
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
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...
Fleury's spanning dimension and chain conditions on non-essential elements in modular lattices
Based on a lattice-theoretic approach, we give a complete characterization of modules with Fleury's spanning dimension. An example of a non-Artinian, non-hollow module satisfying this finiteness condition is constructed. Furthermore we introduce and characterize the dual notion of Fleury's spanning dimension.
Formality of the complements of subspace arrangements with geometric lattices.
Fractal construction of an atomic Archimedean effect algebra with non-atomic subalgebra of sharp elements
Does there exist an atomic Archimedean lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question is given.
Freely adjoining a complement to a lattice
Functional completeness in pseudocomplemented de Morgan algebras
-supplemented property in the lattices
Let be a lattice with the greatest element . Following the concept of generalized small subfilter, we define -supplemented filters and investigate the basic properties and possible structures of these filters.
Generalizations of Boolean algebras. An attribute exploration
Generalized difference posets and orthoalgebras.
Generalized -lattices of order ω+
Generating semigroups for complete atomistic ortholattices.
Generators of existence varieties of regular rings and complemented Arguesian lattices
We proved in an earlier work that any existence variety of regular algebras is generated by its simple unital Artinian members, while any existence variety of Arguesian sectionally complemented lattices is generated by its simple members of finite length. A characterization of the class of simple unital Artinian members [members of finite length, respectively] of such varieties is given in the present paper.
Gleason theorem for signed measures with infinite values