I'm noticing that "in the refrigerator" is "în frigider", not "în frigiderul". Is there a general rule that nouns don't get definite articles after prepositions?
Yes, specifically, the rule states: "In Romanian, a non-modified noun preceded by a preposition (except "cu"!) is necessarily used without the definite article." In "cuptorul," the definite article is expressed by the suffic "ul", which according to this rule is dropped.
However, when the noun is qualified by an adjective, a participle, or a relative clause, the definite article is not used.
Mă îndrept către parc. (I head toward the park.)
Mă îndrept către parcul înverzit. (I head toward the green park.)
And if the qualifying word comes first, it takes the definite article and the following noun does not: "Mă îndrept către înverzitul parc." ("I head toward the green park" -- the same meaning as in the previous example.)
I hope this helps!
The preposition "cu" (with, by means of) is the exception to this: "cu frigiderul."