To get Ahzidal's Ring of Necromancy, you need to have progressed Unearthed to the second stage of the Excavation. In the room with a dead miner on a blood ritual stone, there will be a lever hidden behind some shelves with Soul Gems on them. Pull the lever and the wall behind you will open revealing the ring. To get Ahzidal's Ring of Arcana, you need to activate all the pressure plates in the room with the gate blocking your access to the ring. This can be done by either utilizing the Whirlwind Sprint or Slow Time shout. You will need to use one of these two to complete the puzzle. It is extremely difficult to activate all the plates in time otherwise. Alternatively, you can get the Ring of Arcana by using Telekinesis to pull it towards you, allowing you to loot it through the gate.