Theorems · Definition · ring theory
SkewMonoidAlgebra.erase
{M : Type u_4} → {α : Type u_5} → [inst : AddCommMonoid M] → α → SkewMonoidAlgebra M α →+ SkewMonoidAlgebra M αGiven an element f of a skew monoid algebra, erase a f is an element with the same coefficients
as f except at a where the coefficient is 0.
If a is not in the support of f then erase a f = f.
- Defined in
- Mathlib.Algebra.SkewMonoidAlgebra.Single
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomstatement · cited by 3,230
- SkewMonoidAlgebrastatement and proof · cited by 216
- SkewMonoidAlgebra.coeffproof · cited by 110
- Finsupp.eraseproof · cited by 46
Cited by13
Results whose statement or proof uses this declaration.
- SkewPolynomial.eraseproof · cited by 8
- SkewMonoidAlgebra.coeff_erase_applystatement and proof · cited by 4
- SkewMonoidAlgebra.single_add_erasestatement and proof · cited by 2
- SkewMonoidAlgebra.support_erasestatement · cited by 2
- SkewMonoidAlgebra.erase_singlestatement · cited by 1
- SkewMonoidAlgebra.inductionproof · cited by 1
- SkewPolynomial.support_eraseproof · cited by 1
- SkewMonoidAlgebra.erase_apply_toFinsuppstatement · cited by 0
- SkewMonoidAlgebra.coeff_erase_nestatement · cited by 0
- SkewMonoidAlgebra.coeff_erase_samestatement · cited by 0
- SkewMonoidAlgebra.update_eq_erase_add_singlestatement and proof · cited by 0
- SkewPolynomial.erase_zeroproof · cited by 0