"The man has a wife."
Translation:Mannen har en kone.
Yes. Ei is the feminine indefinite article (as well as meaning not (ikke) if you are a bit old-fashioned, the sentence could then mean The man does not have a wife..).
Kone can be both masculine and feminine, apparently all feminine nouns can be written as masculine (it sure makes grammar a lot easier, with just two genders to remember). I say apparently because my own dialect likes forms and terms ending with open a's and I just abhor the idea of excluding the feminine nouns.
We could also say that the article "en" is for the common gender where masculine and feminine have fused to one gender. This is the case with Swedish and Danish where there are only two genders, common and neutral (et / ett). "En kone" is used in Bokmål because of the strong Danish influence during the centuries of Danish rule. "Ei kone" has been brought back to the written language from the colloquial speech, partly because of efforts to bring Bokmål and Nynorsk (New Norwegian, the other literary tongue of Norwegian) closer to each other. Conservative Bokmål speakers do not accept such "vulgar" forms as "ei kone", and insist on using only two articles, "en" and "et". This conservative form of Bokmål is called Riksmål. Native Norwegian speakers may correct, if this is not the situation anymore.
Hm... Not really... "Ei" is either the indefinite article for feminine nouns, and the language had maskuline, feminine & neuter nouns & articles way back in the time of the Vikings...
Or, it's a negation (same as "ikke"), which was also in use in the Old Norse language.
So no, it's not a result of the Danish influence from the 14th century onwards. But Old Norse was a common language for Norway, Denmark, Sweden & beyond - so in that sense the Danes can probably take parts of the blame...