Radical subgroups of lattice ordered groups
Representation of algebraic distributive lattices with ℵ1 compact elements as ideal lattices of regular rings.
We prove the following result: Theorem. Every algebraic distributive lattice D with at most ℵ1 compact elements is isomorphic to the ideal lattice of a von Neumann regular ring R.(By earlier results of the author, the ℵ1 bound is optimal.) Therefore, D is also isomorphic to the congruence lattice of a sectionally complemented modular lattice L, namely, the principal right ideal lattice of R. Furthermore, if the largest element of D is compact, then one can assume that R is unital, respectively,...
Representations of finite lattices by orders on finite sets
Representations of locally distributive lattices
Representations of ordered semigroups and lattices by binary relations
Representative properties of the quasi-ordered set
Representing lattices by homotopy groups of graphs
In this paper we represent every lattice by subgroups of free groups using the concept of the homotopy group of a graph.