Theorems · Theorem · commutative algebra
monomial_mem_adjoin_monomial
∀ {R : Type u} [inst : CommRing R] {I : Ideal R} {n : ℕ} {r : R},
r ∈ I ^ n → (Polynomial.monomial n) r ∈ Algebra.adjoin R ↑(Submodule.map (Polynomial.monomial 1) I)- Defined in
- Mathlib.RingTheory.ReesAlgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement · cited by 7,192
- Polynomialstatement and proof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- add_commproof · cited by 1,535
- Subalgebrastatement · cited by 1,353
- map_addproof · cited by 964
- Submodule.mapstatement and proof · cited by 614
Cited by1
Results whose statement or proof uses this declaration.
- adjoin_monomial_eq_reesAlgebraproof · cited by 1