The concept of multidimensionality allows to specify contrary variants of a content object on a common, abstract level. This prevents redundancy, simplifies the maintenance and increases the adaptability of content. This is crucial for automated cross media delivery. Though some implementations of multidimensional document systems are available, existing formalisms do not yet cover this concept. This article presents the multidimensional extension of a document algebra, as well as a reference implementation of this algebra in an authoring tool. The algebraic approach is a valuable basis for interoperability of formats and tools in order to realize the whole content workflow in cross media publishing.