comm_alg

SLMath collaboration for adding Krull dimension and Hilbert polynomial to mathlib

We start the comm algebra project by important definitions and theorems and go from there. Feel free to add, modify, and expand this file. Below are starting point for the project:

Definitions of an ideal, prime ideal, and maximal ideal Definition of a Spec of a ring Definition of a Noetherian and Artinian rings Definition of a local ring and quotient ring Definition of the Krull dimension

Give examples of each of the above cases for a particular instances of ring

Theorem 0: Hilbert Basis Theorem Theorem 1: If A is a nonzero ring, then dim A[t] >= dim A +1 Theorem 2: If A is a nonzero noetherian ring, then dim A[t] = dim A + 1 Theorem 3: If A is nonzero ring then dim A_p + dim A/p <= dim A