On duality of submodule lattices
An elementary proof is given for Hutchinson's duality theorem, which states that if a lattice identity λ holds in all submodule lattices of modules over a ring R with unit element then so does the dual of λ.
On modularity in lattices of congruences on ordered sets
On projective intervals in a modular lattice
In this paper a combinatorial result concerning paire of projective intervals of a modular lattice will be established.
On skew lattices. II.
On strong uniform dimension of locally finite groups
We give the description of locally finite groups with strongly balanced subgroup lattices and we prove that the strong uniform dimension of such groups exists. Moreover we show how to determine this dimension.
On the existence of super-decomposable pure-injective modules over strongly simply connected algebras of non-polynomial growth
Assume that k is a field of characteristic different from 2. We show that if Γ is a strongly simply connected k-algebra of non-polynomial growth, then there exists a special family of pointed Γ-modules, called an independent pair of dense chains of pointed modules. Then it follows by a result of Ziegler that Γ admits a super-decomposable pure-injective module if k is a countable field.
On the Kurosh-Ore replacement property
On The Modularity Of Some Orderable Cross-Lattices
On the rhomboidal heredity in ideal lattices
We show that the class of principal ideals and the class of semiprime ideals are rhomboidal hereditary in the class of modular lattices. Similar results are presented for the class of ideals with forbidden exterior quotients and for the class of prime ideals.
On the Word Problem for the Modular Lattice with Four Free Generators.
On uniform dimensions of finite groups
Let G be any finite group and L(G) the lattice of all subgroups of G. If L(G) is strongly balanced (globally permutable) then we observe that the uniform dimension and the strong uniform dimension of L(G) are well defined, and we show how to calculate these dimensions.
Operations on graphs determining congruences on graphs
Ordres "C.A.C."
Orthogonality and complementation in the lattice of subspaces of a finite vector space
We investigate the lattice of subspaces of an -dimensional vector space over a finite field with a prime power together with the unary operation of orthogonality. It is well-known that this lattice is modular and that the orthogonality is an antitone involution. The lattice satisfies the chain condition and we determine the number of covers of its elements, especially the number of its atoms. We characterize when orthogonality is a complementation and hence when is orthomodular. For...
Perfect Elements in the Free Modular Lattices.
Physical states on quantum logics. I
Power series developments in lattice ordered semigroups.
Proper congruences do not imply a modular congruence lattice
Remarks on Ideals in Join-Semilattices.
Representations of finite lattices by orders on finite sets