I do not have any tools are messages I need to list in the ToolAreaRight area of the Applicaion Menu on the Ribbon. I would like to know if there is anyway to turn off just the ToolAreaRight?
There is no way to disable the right tool area completely. You can submit a feature request for this ability: http://devcenter.infragistics.com/Protected/RequestFeature.aspx.
You can just set the MaxWidth property to 2 and MinWidth property to 1 on Ribbon->ApplicationMenu->ToolAreaRight. I don't know if they have some other property to disable it completely.