Theorems · Theorem · commutative algebra
IsRegular.monomial
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {m : σ →₀ ℕ} {a : R},
IsRegular a → IsRegular ((MvPolynomial.monomial m) a)- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.coeffproof · cited by 315
- MvPolynomial.monomialstatement and proof · cited by 253
- IsRegularstatement and proof · cited by 116
- MvPolynomial.extproof · cited by 61
- IsRegular.leftproof · cited by 39
- MvPolynomial.coeff_monomial_mulproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.monomial_one_mul_cancel_left_iffproof · cited by 1
- MvPolynomial.monomial_one_mul_cancel_right_iffproof · cited by 1