What is the official name for a Field Series in mathematics/physics?

I've been working on developing infinitesimal recursion (what I call continuous hierarchy), but I ended up arriving at "field series" instead. My searches didn't seem to come up with anything reasonable (battlefield the video game series), so I'm wondering what the official name for a field series is. Thanks!

What do you mean by field and what by series? Fields are certain rings, and related ones are sometimes a tower of fields or a sequence of fields in case they are contained in one another.

Needs to be user defined.