Translation of monogamia

I learned Russian during 8 years in highschool, but since I left school 6 years ago, I have forgotten most of it and did not have opportunity to speak or practice in any way. That's why I am on Vocabulix.
I had never heard the phrase before. In America, there are also different idioms than here in England. It seems that the Americans say it differently than we do here in the United Kingdom.
I'm learning Spanish, I have been dating a girl in Peru a few months ago, but, unfortunately, she speaks only Spanish. If everything goes well I will move there! For true love I'm ready to do a lot.