It is either Riga (Protestant) Cathedral or Rigas Doms. 'Dome' is meaningless in English - it just means cupola, which this wonderful building has not got. The Riga Russian Orthodox Cathedral has a dome - perhaps you are confusing the two buildings?
The great cathedral of Riga is one of the most beautiful churches of Northern Europe. But when will the Latvians learn that 'Dom' or 'Doms' does not translate as 'Dome' in English? In English it is Riga Cathedral, or the Riga 'Doms', if you want to stick to Latvian.
I visit Riga almost every year and the Dome Cathedral is the first place i visit every time i am in Riga! The Organ music and the beauty of the cathedral is making me cry every single time! the most exciting place on earth (at least for me)!