Kosinguläre und Kleine Moduln#

^#Communicated by A. Facchini.

The submodule in its injective hull is small } is investigated by Talebi und Vanaja (2002) for every R-module M. We solve the three problems which were put forth in that work by replacing the submodule over every commutative Noetherian ring R by the submodule C(M) = ∩ {U ⊂ M | M/U is cosingular }, which is easier to calculate. We give criteria for M/C (M) being cosingular or C ² (M) = C ³ (M), respectively. Every R-module M satisfies and we characterise those rings R over which .

Keywords:

• Coassociated prime ideals
• Cosingular modules
• Matlis duality
• Singular models
• Small modules

Mathematics Subject Classification (2000):

• 13A10
• 13B35
• 13C05
• 13F05

Notes

^#Communicated by A. Facchini.