Learn Hardcore Russian: Я купил помидоры у продавца на рынке. - I bought tomatoes from the vendor at the market.

Because помидоры is the direct object of the verb купил (“I bought”). In Russian, direct objects take the accusative case. Since помидоры is an inanimate plural noun, its accusative form is identical to its nominative form (both помидоры).

What does the preposition у indicate in купил помидоры у продавца?

The preposition у with the genitive case expresses the source or the person you get something from. Here, купил у продавца means “bought from the seller.” It always uses genitive, so продавец becomes продавца.

Why is продавец changed to продавца?

Because the preposition у requires the genitive case. Продавец (nominative singular) becomes продавца (genitive singular).

What case is на рынке, and why use it here?

Here на indicates location (“where?”), so it takes the prepositional case. Рынок (nominative) becomes рынке in prepositional singular: на рынке means “at the market.” If you meant “to the market” (direction), you’d use the accusative: на рынок.