If that's the first mention of the dictionary then "a" is appropriate.
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IvanhrI bought my house 5 years ago. (nothing prevents you from saying this, right?)Right, but I think the comparison may be faulty. I think you need to compare to
CalifJimI lost my dictionary that I bought yesterday.What do you think of this explanation:
It seems to me that you can't have both a possessive expression and a relative clause modifying the same noun, but it's not clear to me why.
sarcandraWhat do you think of this explanation:
In such a sentence structure, "that" modifies or restricts the identity of "dictionary," but because of the possessive "my," that identity has already been defined (if I say "my dictionary," that's the only one I have). The second half should therefore be a nonrestrictive clause:
I lost my dictionary, which I bought