Riven is all about AD. Generally speaking items like Mallet and Atma's aren't bad, but have build paths that don't give her much return while she's building them. When you consider that Riven gains survivability through additional AD you understand why that's a bit counterproductive.
A good build for Riven is like, boots, 2-3 doran's, BF sword->bloodthirster, finishing your boots, then choosing between:
Maw of Malmortius, Guardian Angel, additional Bloodthirsters, or Last Whisper.
Any defensive items should be cheap or have additional AD, like Aegis of the Legion. Frozen Mallet is an OK item on Dominion, or if you find you're getting kited a LOT, but it's very expensive and only gives 20 AD. AD is more cost-effective on Riven than pure health so if you buy mallet you're buying it for the active. Generally just trying to have red buff is better than buying a Mallet.
Generally, my build (sans doran's blades) has been:
Boots, Bloodthirster, Maw/GA (in whatever order is appropriate), Last Whisper+two defensive items, usually Aegis/another BT.