The Compatibility, Independence, and Linear Growth Properties

The first part is about primary decomposition. After reviewing the basic definitions, we survey the compatibility, independence, and linear growth properties that have been known. Then, we prove the linear growth property of primary decomposition for a new family of modules. In the remaining sections, we study secondary representation, which can be viewed as a dual of primary decomposition. Correspondingly, we study the compatibility, independence, and linear growth properties of secondary representations.