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@ -9,6 +9,8 @@ Feel free to add, modify, and expand this file. Below are starting points for th
- Definitions of an ideal, prime ideal, and maximal ideal: - Definitions of an ideal, prime ideal, and maximal ideal:
```lean ```lean
def Mathlib.RingTheory.Ideal.Basic.Ideal (R : Type u) [Semiring R] := Submodule R R def Mathlib.RingTheory.Ideal.Basic.Ideal (R : Type u) [Semiring R] := Submodule R R
class Mathlib.RingTheory.Ideal.Basic.IsPrime (I : Ideal α) : Prop
class IsMaximal (I : Ideal α) : Prop
``` ```
- Definition of a Spec of a ring: `Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic.PrimeSpectrum` - Definition of a Spec of a ring: `Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic.PrimeSpectrum`
@ -31,7 +33,7 @@ Give Examples of each of the above cases for a particular instances of ring
Theorem 0: Hilbert Basis Theorem: Theorem 0: Hilbert Basis Theorem:
```lean ```lean
instance isNoetherianRing [Finite σ] [IsNoetherianRing R] : IsNoetherianRing (MvPolynomial σ R) theorem Mathlib.RingTheory.Polynomial.Basic.Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNoetherianRing R[X]
``` ```
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