Theorems · Definition · commutative algebra
AdjoinRoot.modByMonicHom
{R : Type u_1} → [inst : CommRing R] → {g : Polynomial R} → g.Monic → AdjoinRoot g →ₗ[R] Polynomial RAdjoinRoot.modByMonicHom sends the equivalence class of f mod g to f %ₘ g.
This is a well-defined right inverse to AdjoinRoot.mk, see AdjoinRoot.mk_leftInverse.
- Defined in
- Mathlib.RingTheory.AdjoinRoot
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 124 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- LinearMap.compproof · cited by 1,642
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.toLinearMapproof · cited by 1,171
- Ideal.spanproof · cited by 948
- Polynomial.Monicstatement and proof · cited by 461
- Submodule.restrictScalarsproof · cited by 180
- AdjoinRootstatement · cited by 177
- Submodule.liftQproof · cited by 36
Cited by5
Results whose statement or proof uses this declaration.
- AdjoinRoot.powerBasisAux'proof · cited by 2
- AdjoinRoot.modByMonicHom_mkstatement · cited by 1
- AdjoinRoot.powerBasisAux'_repr_apply_to_funstatement · cited by 0
- AdjoinRoot.mk_leftInversestatement · cited by 0
- AdjoinRoot.modByMonicHom.congr_simpstatement and proof · cited by 0