I have encountered this sentence:
Ich hatte trotz vieler Jahre Englischunterricht in der Schule Probleme mit der Sprache.
I know this type of genitive, where the word doesn't have an article:
Das ist die schönste Stadt Deutschlands.
Now my question is, in the first sentence why isn't an "s" added to the end of the word "Englischunterricht". Is this word really in genitive form? I know that genitive is the following:
eines Unterrichts, des Unterrichts
But what I wrote just now has an article. What if the word is intended to be in the genitive case but doesn't have an article (regardless whether it is definite or indefinite)?