Theorems · Theorem · commutative algebra
ringKrullDim_succ_le_ringKrullDim_polynomial
∀ {R : Type u_1} [inst : CommRing R], ringKrullDim R + 1 ≤ ringKrullDim (Polynomial R)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 111 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement · cited by 5,681
- ENatstatement · cited by 4,985
- Polynomial.Cproof · cited by 1,598
- WithBotstatement · cited by 1,498
- ringKrullDimstatement · cited by 75
- Polynomial.coeff_C_zeroproof · cited by 58
- Polynomial.coeff_X_zeroproof · cited by 48
- Polynomial.constantCoeffproof · cited by 15
- ringKrullDim_succ_le_of_surjectiveproof · cited by 2
- Polynomial.X_mem_nonzeroDivisorsproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.ringKrullDim_of_isNoetherianRingproof · cited by 1
- ringKrullDim_add_natCard_le_ringKrullDim_mvPolynomialproof · cited by 1