Untersuchung spezieller Idealverbände. (Investigation of special ideal lattices) (Q1825212)

Let L be a lattice and I(L) its ideal lattice. It is well known that I(L) is modular (resp. distributive) if and only if L is modular (resp. distributive). In the present paper, the author proves some results on I(L) for some other classes of lattices, e.g. semimodular lattices, lattices with chain conditions, and X-lattices (i.e. complete lattices L with \(L=\{\bigvee X':\) \(X'\subseteq X\})\) for some special sets X (e.g. the sets of all compact elements, join irreducible elements, atoms).