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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.

3 votes

analogue of a set with n binary operations

The study of sets with an arbitrary number of operations is called universal algebra. Also universal algebra isn't limited to binary operations but studies operations of any arity: nullary, unary, bi …
Roy Maclean's user avatar
  • 1,190
4 votes

Modern algebraic geometry vs. classical algebraic geometry

Depends what you mean by "modern". "Numerical algebraic geometry" using homotopy methods is modern but concrete. "Introduction to numerical algebraic geometry", A Sommese, J Verschelde, C Wampler ht …