SinTan1729/comm_alg
1
0
Fork 0
mirror of https://github.com/GTBarkley/comm_alg.git synced 2024-12-26 07:38:36 -06:00
Code Issues Projects Releases Packages Wiki Activity

Update README.md

Browse source 
Formatted the list to make it readable.
This commit is contained in:
ssavkar1 2023-06-09 21:05:03 -07:00 committed by GitHub
parent 73d36c2514
commit accf75c663
No known key found for this signature in database
GPG key ID: 4AEE18F83AFDEB23
1 changed files with 17 additions and 5 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

22
README.md
View file

@ -2,17 +2,29 @@
SLMath collaboration for adding Krull dimension and Hilbert polynomial to mathlib 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. 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: 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 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 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 0: Hilbert Basis Theorem
Theorem 1: If A is a nonzero ring, then dim A[t] >= dim A +1 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 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 Theorem 3: If A is nonzero ring then dim A_p + dim A/p <= dim A