It should be hyphenated when it's being used as an adjective. For example: nineteenth-century writers.
No, "nineteenth-century" should not be capitalized unless it is at the beginning of a sentence or part of a title.
Yes, the compound noun 'nineteenth century' is a common noun, a general word for the one hundred years between 1801-1900; a general word for any point in the 1800s.The word 'nineteenth century' also functions as an adjective.
Eighteen can be both an adjective, meaning one more than seventeen, or a noun meaning the cardinal number that is the sum of seventeen and one.
The nineteenth century was from 1800 - 1899.
Neunzehnte is the word for nineteenth in German.
Nineteenth-Century Literature was created in 1945.
Nineteenth Army - Japan - was created in 1942.
Nineteenth Army - Japan - ended in 1945.
The Nineteenth Century - periodical - was created in 1877.
The Nineteenth Century - periodical - ended in 1972.
Woman in the Nineteenth Century was created in 1843.