Can you have a Roll-up Summary field in the case of a Master–Detail Relationship

Yes. You can have a roll-up summary in case of a master-detail relationship. But not in case of a lookup relationship.
A roll-up summary field is used to display a value in a master record based on the values of a set of fields in a detail record. The detail record must be related to the master through a master-detail relationship.
There are 4 calculations that you can do using roll-up summary field. You can count the number of detail records related to a master record. Or, you can calculate the sum, minimum value, or maximum value of a field in the detail records.

Yes you can implement it