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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
16
votes
Commutative algebra with a view toward algebraic _number theory_
I concur that Neukirch is a good candidate, so instead of starting with a new recommendation (I'll come back to that later), let me instead disagree with Felipe Voloch's contention that algebraic numb …
20
votes
What does primary mean geometrically?
Geometrically, primary ideals (and most importantly, primary decomposition) gives you a way of visualizing, or at least identifying, embedded components in your variety/scheme. In fact, from the geom …