Theorems · Theorem · commutative algebra
MvPolynomial.isUnit_iff_totalDegree_of_isReduced
∀ {σ : Type u_1} {R : Type u_2} [inst : CommRing R] {P : MvPolynomial σ R} [IsReduced R],
IsUnit P ↔ IsUnit (MvPolynomial.coeff 0 P) ∧ P.totalDegree = 0- Defined in
- Mathlib.Algebra.MvPolynomial.Nilpotent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- IsUnitstatement and proof · cited by 1,602
- MvPolynomial.coeffstatement and proof · cited by 315
- IsNilpotentproof · cited by 248
- IsReducedstatement and proof · cited by 98
- MvPolynomial.totalDegreestatement and proof · cited by 76
- not_imp_commproof · cited by 56
- MvPolynomial.totalDegree_eq_zero_iffproof · cited by 3
- MvPolynomial.isUnit_iffproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- MvPolynomial.irreducible_of_forall_totalDegree_leproof · cited by 1
- MvPolynomial.irreducible_of_totalDegree_eq_oneproof · cited by 1
- MvPolynomial.isUnit_iff_eq_C_of_isReducedproof · cited by 0