Narrow Results

We present a characterization of l-ideals in an arbitrary l-group without use of inequalities, which generalizes the corresponding result of Alpay, Emel'yanov and Ercan for o-ideals in Riesz spaces.

The concept of σ-ideals is introduced in almost distributive lattices (ADLs). Generalized stone ADLs are characterized in terms of their σ-ideals and α-ideals. Normal ADLs are also characterized in terms of their O-ideals and σ-ideals. Finally, a discussion is made about the epimorphic images and inverse images of σ-ideals.

The notion of quasicomplemented C-algebras is introduced. The concepts of strong α-ideals and O-ideals are introduced and then some properties of quasicomplemented C-algebras are studied with the help of strong α-ideals and O-ideals. The concept of regular C-algebras is introduced and also some equivalent conditions are derived for every regular C-algebra to become a quasicomplemented C-algebra. Some topological characterizations are considered for quasicomplemented C-algebras and regular C-algebras.