Guess the index term
 

Here's an idea for another forum game. Many books have index lists in the back that looks like:
sequence
--- bounded page ###
--- Cauchy page ###
--- convergent page ###
--- monotonic page ###
etc. One can post the 'bounded' til 'monotonic' part, and others will try to guess 'sequence'.

So one person looks in the index of a textbook and finds an index listing with multiple sub-listings. They post a picture of just the sub-listing, and others guess what the super listing is.

To start:

They take 29 pages to get from valuation ___ to discrete valuation ___? :smile:

I guess "group".

The sublistings "local --," "semilocal --," "valuation --," "discrete valuation --," and especially "quotient --" and most especially "-- of fractions," tell me they are subtopics of "field."

The sublistings "(semi)local --" and "(discrete) valuation --" can also be subtopics of "ring." I'm not sure about "graded" and "absolutely flat" WRT fields, though I have seen them WRT "modules." I have seen "quotient ring" used to indicate the modulo arithmetic of a ring modulo an ideal. The listings "sub --" and "-- homomorphism" fit too many topics for me to try to list them all.

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