Theorems · Theorem · ring theory
AddMonoidAlgebra.supported_eq_span_single
∀ (R : Type u_1) {M : Type u_3} [inst : Semiring R] (s : Set M),
AddMonoidAlgebra.supported R R s = Submodule.span R ((fun m => AddMonoidAlgebra.single m 1) '' s)- Defined in
- Mathlib.Algebra.MonoidAlgebra.Module
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 82 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Submodulestatement · cited by 7,192
- Set.imagestatement and proof · cited by 5,609
- Finsuppproof · cited by 5,255
- Submodule.spanstatement and proof · cited by 1,504
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.toLinearMapproof · cited by 1,171
- Finsupp.singleproof · cited by 943
- AddMonoidAlgebrastatement · cited by 649
- Set.image_congrproof · cited by 533
- AddMonoidAlgebra.singlestatement and proof · cited by 250
Cited by5
Results whose statement or proof uses this declaration.
- MvPolynomial.restrictSupport_eq_spanproof · cited by 3
- MvPolynomial.IsWeightedHomogeneous.induction_onproof · cited by 1
- MvPolynomial.IsWeightedHomogeneous.pderivproof · cited by 1
- MvPolynomial.homogeneousSubmodule_one_eq_span_Xproof · cited by 1
- MvPolynomial.IsWeightedHomogeneous.sum_weight_X_mul_pderivproof · cited by 1