mirror of
https://github.com/GTBarkley/comm_alg.git
synced 2024-12-26 23:48:36 -06:00
33 lines
1.1 KiB
Markdown
33 lines
1.1 KiB
Markdown
# Commutative algebra in Lean
|
|
|
|
Welcome to the repository for adding definitions and theorems related to Krull dimension and Hilbert polynomials to mathlib.
|
|
|
|
We start the commutative algebra project with a list of important definitions and theorems and go from there.
|
|
|
|
Feel free to add, modify, and expand this file. Below are starting points 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
|
|
|
|
Definitions of a local ring and quotient ring
|
|
|
|
Definition of the chain of prime ideals and the length of these chains
|
|
|
|
Definition of the Krull dimension (supremum of the lengh of chain of prime ideal)
|
|
|
|
Definition of the height of prime ideal (dimension of A_p)
|
|
|
|
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
|
|
|
|
Definition of a graded module
|