Rings of Brighthearth can copy Basalt Monolith's : Untap this artifact activated ability because that ability is not a mana ability, but Rings cannot copy Basalt Monolith's : Add because that is a mana ability (Rings' oracle text). You activate Basalt Monolith's : Untap this artifact, may pay for Rings to copy it, and the copy and original will be put on the stack (Rings' oracle text.. Like Basalt Monolith + Rings of Brighthearth for endless ; combine them with Myr Matrix to get as many 1/1 dudes as you want or with a Sensei's Divining Top and/or Staff of Domination to just draw the entire deck until you reach your wincon. The Monolith also pairs well with the already included Forsaken Monument; goes infinite without the Rings.
null Infinite cascade with mana value equal to the next spell you cast. Stack is currently untap monolith, untap monolith. Step 4. Resolve only 1 of the 2 untap triggers. Step 5. Tap monolith for 3 mana and use 2 of it for rings of brighthearth to copy the original untap trigger. You are now +1 mana, with 2 untap triggers on the stack. Repeat steps 4 and 5 as many times as mana you need.