Ummm, sorry burst an infinite combo, but specifies a "non mana ability" and the monolith is a mana ability, hence, you tap it for mana.

Ummm, sorry burst an infinite combo, but rings specifies a "non mana ability" and the monolith is a mana ability, hence, you tap it for mana.

Sorry for double post, phone glitches out.

Rings of Brighthearth copies the "3 colorless: untap Basalt Monolith," not the mana ability. This passage is from the wizards forum:

For those who don't know how the brighthearth combo works, here it is:

1. Basalt Monolith is tapped and you have 5 floating.

2. Pay 3 to put the "Untap Basalt Monolith" on the stack.

3. Pay 2 to put a copy of "Untap Basalt Monolith" on the stack.

Stack starts resolving.

1. Resolve the copy of "Untap Basalt Monolith" and Basalt Monolith untaps.

2. Tap Basalt Monolith for 3. Abilities that add mana to your mana pool don't use the stack. You get the mana immediately. Basalt Monolith is now tapped.

3. Resolve the original "Untap Basalt Monolith" and Basalt Monolith untaps.

4. Now tap Basalt Monolith for 3 you now have Basalt Monolith tapped and you have 6 floating and you are back to your starting position with 1 extra mana.

And link it up with Mycosynth Lattice and all that mana now has a use.