Erzeugendensysteme und der A-Dimensionssatz in Atomaren Modularen Verbänden

In atomic modular lattices a special dimension can be introduced by atoms. The question was, whether the dimensional formula holds. Trying to prove this leads to a problem, formulated by Olaf Tamaschke (see [5]). It is shown here that an additional property is necessary, called atomic closed (atomar abgeschlossen). With this quality some new theorems can be proved. For instance: lattices not being atomic closed contain a special sublattice, and in lattices of finite length this property is equivalent to the validity of the dimensional formula.