Ranrike or Rånrike (Old Norse Ránríki) was the old name for a part of Viken, corresponding to southeast Norway (Oslofjord area) and the northern half of the modern Swedish (Norwegian until 1658) province of Bohuslän (roughly identical with Álfheimr of Scandinavian mythology). When folklore and culture is concerned the usage has been revived to refer to northern Bohuslän.
The name Ranrike is sometimes said to have derived its name from Old Norse goddess of the sea, Rán. There is no clear etymology of Rán. As the Indo-Europeans did not have a word for 'sea', it may not be Indo-European, in which case it would be older than the Nordics in the region. Jordanes does give us a terminus ante quem for the use of Ragnaricii/Ranii: One king, Rodwulf of the Ranii (identified by some with Ranrike), had left his kingdom to join Theodoric the Great in Ravenna.
There is a possible parallel in the name Hålogaland, if the name means "sacred land" or "land of the sacred". In any case, the position of Ragnaricii next to Raumaricii (Romerike) indicates that it is probably the same as Ranrike, believed to be named after the goddess of the sea, Rán (Ran-riki, "reich of Ran or Rån"). Another parallel supports this derivation: Pliny the Elder's Saevo mountain range, probably meaning "sea land", refers in part to Ranrike (see under Scandinavia). Moreover, Rán is the name of a dangerous goddess, who raises storms at sea and collects the drowned in her net. Such a name support the "dangerous island" etymology of Scandinavia. However, this pattern is only a web of speculation.