Theorems · Theorem · commutative algebra
MvPowerSeries.monomial_mem_nonzeroDivisors
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] {n : σ →₀ ℕ} {r : R},
(MvPowerSeries.monomial n) r ∈ nonZeroDivisors (MvPowerSeries σ R) ↔ r ∈ nonZeroDivisors R- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- Submonoidstatement · cited by 3,086
- nonZeroDivisorsstatement · cited by 895
- MvPowerSeriesstatement · cited by 659
- MvPowerSeries.monomialstatement · cited by 69
- Iff.andproof · cited by 33
- MvPowerSeries.monomial_mem_nonzeroDivisorsLeftproof · cited by 1
- MvPowerSeries.monomial_mem_nonzeroDivisorsRightproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MvPowerSeries.X_mem_nonzeroDivisorsproof · cited by 1