Where does “Ερυθραία” come from?

Ερυθραία (Greek) comes from Italian Eritrea, from Latin Erythraea, from Ancient Greek Ἐρυθραία, from Ancient Greek Ἐρυθραῖος, from Ancient Greek Ἐρυθραί, from Ancient Greek ἐρυθρός, from Proto-Hellenic *erutʰrós.

Ερυθραία (Greek): Eritrean

Definitions

Eritrean

Ancestry of “Ερυθραία”, step by step

Step	Language	Word	Meaning
1	Italian	Eritrea	—
2	Latin	Erythraea	the territory of Erythrae, Beotia
3	Ancient Greek	Ἐρυθραία	Erythraea or Eritrea
4	Ancient Greek	Ἐρυθραῖος	—
5	Ancient Greek	Ἐρυθραί	Erythrae; Ildırı, Turkey
6	Ancient Greek	ἐρυθρός	reddish, red
7	Proto-Hellenic	*erutʰrós	—

Every word from Proto-Hellenic *erutʰrós →Every word from Ancient Greek ἐρυθρός →Every word from Ancient Greek Ἐρυθραί →