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To access the Administration → Alert Configuration area you need to have a role with the Manage version of the Alert configuration permission. If you only have the View version of this permission, you will not be able to perform any task here (more info about permissions here).
Additionally, you need to have alerts assigned (see Assign resources to a role). You will only see alert definitions for those alerts assigned and allowing only the interaction level specified for them. In other words, the permissions grants theoretical access to alerts while assigning a specific alert grants the actual access.
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