Why are ring extensions only discussed in the context of $\mathbb{C}$?

Question

I'm watching the great (imo) set of lectures on abstract algebra from the harvard extension school that's available on youtube.

Now this lecture is about extending a ring. The lecturer talk about this in the context of extending subrings of $\mathbb{C}$. However, I wonder (as did someone during the lecture but the prof didn't really answer the question) why this is only discussed in the context of subrings of $\mathbb{C}$. But couldn't the same constructions also be made in more general rings? Where a subring of an arbitrary ring is extended by just adjoining some elements from the large ring?

Thanks

Answer 1

Never mind, just a little bit later he explains that it is indeed not limited to $\mathbb{C}$, I should have been a little bit more patient.