On Shifted Principles of Generalized Local Cohomology Modules

In this paper, we study the structure of attached prime ideals of generalized local cohomology modules. We show the Shifted Localization Principle, the Weak General Shifted Localization Principle and the Shifted Completion Principle for generalized local cohomology modules. We introduce a generalization of pseudo-support and pseudo-dimension using the generalized local cohomology modules and we show that pseudo-support is closed under certain conditions. As applications, we investigate the top non-vanishing and the associativity formula for multiplicities of generalized local cohomology modules.