Importance of Complete ring of Qoutients

Dear NG,

I just recently touched subjects involving Complete ring of Qoutients
and I was wondering if someone could motivate me on why this is somehow
important to algebraists. For reduced rings I think they contain the
ring itself and that they have nice properties like being Baer and Von
Neumann regular and etc. and therefore they allow us to conclude that a
Baer, Von Neumann regular hull .. etc. exists for such rings (or maybe
Im wrong, please correct me if so). But are there more into it? I
suppose this is one of the things that would be extensively used in
homology algebra, or not? Why are dense ideals so important? I would be
grateful if someone could throw some words of motivation/inspiration
for such rings and their constructions.

Sincerely,
Jose Capco

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