mirror of
https://github.com/GTBarkley/comm_alg.git
synced 2024-12-26 07:38:36 -06:00
Update README.md
Formatted the list to make it readable.
This commit is contained in:
parent
73d36c2514
commit
accf75c663
1 changed files with 17 additions and 5 deletions
22
README.md
22
README.md
|
@ -2,17 +2,29 @@
|
|||
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
|
||||
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
|
||||
|
|
Loading…
Reference in a new issue