A linear property of Goldie dimension of modules and modular lattices.
The Goldie dimension is a generalization of the linear dimension of linear spaces. As a basis of a linear space is characterized as a minimal generating subset of the space, the aim of this paper is to study how far this characterization can be extended to the Goldie dimension. In this paper the author studies the Goldie dimension of modular lattices with 0. The author introduces generating subsets of lattices. The main theorems of this paper describe lattices in which minimal generating subsets are bases and those in which the cardinality of every minimal generating subset is equal to the Goldie dimension. Finally, the results on lattices are applied to modules and to the dual Goldie dimension of lattices and modules.
scientific article; zbMATH DE number 5882444
scientific article