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

carlsondesign
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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!
 
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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.
 

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