AbstractWe show that in the case of 2-dimensional lattices, Quebbemann's notion of modular and strongly modular lattices has a natural extension to the class group of a given discriminant, in terms of a certain set of translations. In particular, a 2-dimensional lattice has “extra” modularities essentially when it has order 4 in the class group. This allows us to determine the conditions on D under which there exists a strongly modular 2-dimensional lattice of discriminant D, as well as how many such lattices there are. The technique also applies to the question of when a lattice can be similar to its even sublattice
A variety (equational class) of lattices is said to be finitely based if there exists a finite set o...
Abstract. In 1968, E. T. Schmidt introduced the M3[D] construction, an extension of the five-element...
A lattice L is said to be dually semimodular if for all elements a and b in L, a ∨ b covers b implie...
AbstractWe show that in the case of 2-dimensional lattices, Quebbemann's notion of modular and stron...
We show that in the case of 2-dimensional lattices, Quebbemann's notion of modular and strongly modu...
AbstractWith any integral lattice Λ in n-dimensional Euclidean space we associate an elementary abel...
With any integral lattice Λ in n-dimensional Euclidean space we associate an elementary abelian 2-gr...
It is shown that an n-dimensional unimodular lattice has minimal norm at most 2[n/24]+2, unless n=23...
AbstractIt is shown that ann-dimensional unimodular lattice has minimal norm at most 2[n/24]+2, unle...
Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices that includes a...
AbstractFinite length 2-distributive modular lattices of finite representation type are characterize...
In lattice theory the two well known equational class of lattices are the distributive lattices and ...
We prove that the congruence lattice of a nilsemigroup is modular if and only if the width of the se...
We prove that the congruence lattice of a nilsemigroup is modular if and only if the width of the se...
AbstractLet V be a discriminator variety such that the class B={A∈V: A is simple and has no trivial ...
A variety (equational class) of lattices is said to be finitely based if there exists a finite set o...
Abstract. In 1968, E. T. Schmidt introduced the M3[D] construction, an extension of the five-element...
A lattice L is said to be dually semimodular if for all elements a and b in L, a ∨ b covers b implie...
AbstractWe show that in the case of 2-dimensional lattices, Quebbemann's notion of modular and stron...
We show that in the case of 2-dimensional lattices, Quebbemann's notion of modular and strongly modu...
AbstractWith any integral lattice Λ in n-dimensional Euclidean space we associate an elementary abel...
With any integral lattice Λ in n-dimensional Euclidean space we associate an elementary abelian 2-gr...
It is shown that an n-dimensional unimodular lattice has minimal norm at most 2[n/24]+2, unless n=23...
AbstractIt is shown that ann-dimensional unimodular lattice has minimal norm at most 2[n/24]+2, unle...
Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices that includes a...
AbstractFinite length 2-distributive modular lattices of finite representation type are characterize...
In lattice theory the two well known equational class of lattices are the distributive lattices and ...
We prove that the congruence lattice of a nilsemigroup is modular if and only if the width of the se...
We prove that the congruence lattice of a nilsemigroup is modular if and only if the width of the se...
AbstractLet V be a discriminator variety such that the class B={A∈V: A is simple and has no trivial ...
A variety (equational class) of lattices is said to be finitely based if there exists a finite set o...
Abstract. In 1968, E. T. Schmidt introduced the M3[D] construction, an extension of the five-element...
A lattice L is said to be dually semimodular if for all elements a and b in L, a ∨ b covers b implie...