A dynamic semiconductor memory and a method for operating such a memory includes memory banks with memory cells disposed in rows, and registers associated with the memory banks for storing an address of an open, activated word line. In the event of an external refresh command, a control device causes, after the refresh operation, the state of the memory banks to be reestablished, in particular, the word line whose address was stored in the register to be reactivated. Such a purely on-chip measure increases the operating speed of the memory.