I've always seen class diagrams with aggregations to other classes elide the associated class from the other classes attribute list. Why is that? Wouldn't it be more clear to always add it?
For example, given a School class and a Department class we might see that depicted like this:
In other words, the department was not shown in the attribute list of School. I always wondered why it was that way as to me, it would be much clearer if it would be added to the attribute list (only have to look in one place to see what the calss has).
There's certainly nothing to prevent you from adding a field to the list of attributes for the aggregation. I think the reason most people don't do it is because it would duplicate other information on the diagram--mainly, the actual association itself.