On pseudocomplemented semilattices with Stone congruence lattices
On radical classes of Abelian linearly ordered groups
On some finite groupoids with distributive subgroupoid lattices
The aim of the paper is to show that if S(G) is distributive, and also G satisfies some additional condition, then the union of any two subgroupoids of G is also a subgroupoid (intuitively, G has to be in some sense a unary algebra).
On subalgebra lattices of a finite unary algebra. II.
We use graph-algebraic results proved in [8] and some results of the graph theory to characterize all pairs of lattices for which there is a finite partial unary algebra such that its weak and strong subalgebra lattices are isomorphic to and , respectively. Next, we describe other pairs of subalgebra lattices (weak and relative, etc.) of a finite unary algebra. Finally, necessary and sufficient conditions are found for quadruples of lattices for which there is a finite unary algebra having...
On the collection of lattices determined by the same poset of meet-irreducibles.
On the congruence lattice of an abelian lattice ordered group
In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.
On the lattice automorphisms of certain simple algebraic groups
On the lattice automorphisms of and
On the modularity of the lattice of fundamental orders on a semilattice.
On the representation of lattices by subsemigroup lattices of bands.
On the subsemilattices of first-order definable and openly first-order definable congruences of the congruence lattice of a universal algebra.
On the surjectivity of the Ribenboim representation of a lattice ordered group.
On varieties of regular -semigroups
On varieties of regular -semigroups, II
On weak direct product decompositions of lattices and graphs
Perfect Elements in the Free Modular Lattices.
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