This is the 2627th most frequent Swedish word.
ryske
"Ryske" means "the Russian" (used as a masculine form in older Swedish).
Here, 'ryske' is used as an adjective in its definite form referring to the nationality (Russian) of the described noun 'författaren' (author).
Den ryske författaren har skrivit många berömda böcker.
The Russian author has written many famous books.
In this sentence, 'ryske' is used erroneously since in the indefinite case, the correct form would be 'rysk'; this could serve as an example for teaching common mistakes.
Under resan träffade vi en ryske diplomat.
During the trip, we met a Russian diplomat.
Similar to the second example, 'ryske' is not correctly applied in this sentence as the noun 'pälsmössa' (fur hat) is an indefinite object, and the correct adjective form is 'rysk'.