Theorems · Theorem · commutative algebra
DividedPowers.dpow_zero
∀ {A : Type u_1} [inst : CommSemiring A] {I : Ideal A} (self : DividedPowers I) {x : A}, x ∈ I → self.dpow 0 x = 1- Defined in
- Mathlib.RingTheory.DividedPowers.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses no axioms
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- DividedPowersstatement and proof · cited by 112
- DividedPowers.dpowstatement · cited by 85
Cited by5
Results whose statement or proof uses this declaration.
- DividedPowers.factorial_mul_dpow_eq_powproof · cited by 5
- DividedPowers.dpow_sumproof · cited by 2
- DividedPowers.isSubDPIdeal_inf_iffproof · cited by 2
- DividedPowers.isDPMorphism_iffproof · cited by 0
- DividedPowers.prod_dpowproof · cited by 0